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The Physics & Technology of

Radiation theRapy

Patrick N. McDerMottcoliN G. ortoN

This textbook is an introduction to the physics and technology used in radiation therapy. It is the outgrowth of a course taught to medical residents in radiation oncology and it has been classroom tested over many years. Every effort has been made to make explanations clear and simple without oversimplifying. The book has been designed to be interesting to read as well as clinically relevant. The first half of the book contains the radiation physics necessary to under-stand radiation therapy. The second half of the book covers the applied phys-ics and technology of radiation therapy. Topics include: treatment machines, beam calibration, dosimetric parameters, MU calculations, dose distributions in patients, electron beams, brachytherapy, radiation safety, quality assurance, imaging, and special modalities.

FEaTUrEs:• Comprehensive end

of chapter summaries

• “Rules of thumb”

• Numerous example-problems

• Full problem set for each chapter with selected answers

• Clinically realistic linac dosimetry data for practice MU calculations

• ABR physician board certification physics topic matrix

• ARRT exam topic matrix

The Physic

s & Tech

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Contents

Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix

Chapter 1 Mathematics Review

1.1 Exponents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21.1.1 Multiplication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-31.1.2 Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-31.1.3 An Exponential Raised to a Power . . . . . . . . . . . . . . . . . . . . . . . 1-31.1.4 A Product Raised to a Power . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-41.1.5 Base e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4

1.2 Logarithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-71.3 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-111.4 Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-17

Chapter 2 Review of Basic Physics

2.1 Units for Physical Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12.2 Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2

2.2.1 Newton’s Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42.2.2 Work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-52.2.3 Work Energy Theorem and Energy Conservation . . . . . . . . . . . . 2-52.2.4 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6

2.3 Electricity and Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-62.3.1 Charge and the Coulomb Force . . . . . . . . . . . . . . . . . . . . . . . . . 2-62.3.2 Electric Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-82.3.3 Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-92.3.4 Potential Difference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-102.3.5 The Electron Volt: A Unit of Energy, Not Voltage . . . . . . . . . . . 2-122.3.6 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-14

2.4 Electromagnetic Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-162.5 The Special Theory of Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-202.6 Review of Atomic Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-29Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-30

vii

Chapter 3 Atomic Nuclei and Radioactivity

3.1 Basic Properties of Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23.2 Four Fundamental Forces of Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-33.3 Nuclear Binding Energy: Mass Defect . . . . . . . . . . . . . . . . . . . . . . . . . 3-53.4 Stability of Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-63.5 Antimatter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-93.6 Properties of Nuclei and Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-93.7 Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-103.8 Mathematics of Radioactive Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-113.9 Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-133.10 Half-Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-143.11 Mean-Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-183.12 Modes of Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-19

3.12.1 Alpha Decay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-193.12.2 Electromagnetic Decay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-193.12.3 Beta Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-20

3.13 Decay Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-243.14 Radioactive Equilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-26

3.14.1 Secular Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-273.14.2 Transient Equilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-28

3.15 Production of Radionuclides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-303.15.1 Fission Byproducts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-303.15.2 Neutron Activation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-323.15.3 Particle Accelerators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-34

Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-35Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-40Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-42

Chapter 4 X-Ray Production I: Technology

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14.2 X-Ray Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24.3 Therapy X-Ray Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-94.4 X-Ray Film and Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-104.5 X-Ray Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19

Chapter 5 X-Ray Production II: Basic Physics and Propertiesof Resulting X-Rays

5.1 Production of X-Rays: Microscopic Physics . . . . . . . . . . . . . . . . . . . . 5-15.1.1 Characteristic X-Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-25.1.2 Bremsstrahlung Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4

viii THE PHYSICS AND TECHNOLOGY OF RADIATION THERAPY

5.2 X-Ray Spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-55.3 Efficiency of X-Ray Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-105.4 Directional Dependence of Bremsstrahlung Emission . . . . . . . . . . . . . 5-125.5 X-Ray Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-12

5.5.1 Beam Divergence and the Inverse-Square Effect . . . . . . . . . . . . 5-145.5.2 Attenuation by Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-16

5.6 Half-Value Layer (HVL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-185.7 Mass Attenuation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-20Appendix: Röntgen and the Discovery of X-Rays. . . . . . . . . . . . . . . . . . . . . . 5-22Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-25Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-28Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-29

Chapter 6 The Interaction of Radiation with Matter

6.1 Photon Interactions With Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-26.1.1 Coherent Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-36.1.2 Photoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-46.1.3 Compton Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-56.1.4 Pair Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-96.1.5 Photonuclear Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-116.1.6 Total Mass Absorption Coefficient . . . . . . . . . . . . . . . . . . . . . . . 6-11

6.2 Interaction of Charged Particles with Matter . . . . . . . . . . . . . . . . . . . . 6-116.2.1 Electron Interactions with Matter. . . . . . . . . . . . . . . . . . . . . . . . 6-146.2.2 Stopping Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-156.2.3 Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-186.2.4 Mean Energy To Produce an Ion Pair. . . . . . . . . . . . . . . . . . . . . 6-206.2.5 Heavy Charged Particle Interactions and the Bragg Peak . . . . . 6-20

6.3 Neutron Interactions with Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-21Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-24Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-27Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-29

Chapter 7 Radiation Measurement Quantities

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-17.2 Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-27.3 Charged Particle Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-47.4 Some Important Radiation Dosimetry Quantities . . . . . . . . . . . . . . . . . 7-47.5 Dose Buildup and Skin Sparing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-97.6 Absorbed Dose to Air. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-137.7 Dose in a Medium Calculated from Exposure . . . . . . . . . . . . . . . . . . . 7-147.8 Dose in Free Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-177.9 An Example of Photon Interactions: History of a 5.0 MeV Photon

in Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-177.10 Monte Carlo Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-20

CONTENTS ix

7.11 Microscopic Biological Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-22Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-24Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-26Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-28

Chapter 8 Radiation Detection and Measurement

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-18.2 Phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-38.3 Gas Ionization Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-5

8.3.1 Ionization Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-58.3.2 Survey Meter Ion Chambers. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-168.3.3 Charge Collection and Measurement . . . . . . . . . . . . . . . . . . . . . 8-178.3.4 Proportional Counters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-218.3.5 Geiger-Müller (GM) Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-228.3.6 Summary of Gas Ionization Detectors . . . . . . . . . . . . . . . . . . . . 8-25

8.4 Solid-State Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-258.4.1 Thermoluminescent Dosimeters . . . . . . . . . . . . . . . . . . . . . . . . . 8-258.4.2 Film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-298.4.3 Diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-338.4.4 MOSFETs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-348.4.5 Polymer Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-36

8.5 Liquid Dosimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-368.5.1 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-368.5.2 Chemical Dosimetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-37


Chapter 9 External Beam Radiation Therapy Units

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-19.2 Medical Electron Linear Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . 9-5

9.2.1 Source of Microwave Power . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-129.2.2 The Treatment Head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-169.2.3 Linear Accelerator Auxiliary Subsystems. . . . . . . . . . . . . . . . . . 9-229.2.4 Interlocks and Safety Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 9-249.2.5 Patient Support Assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-26

9.3 Cobalt-60 Teletherapy Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-269.4 Photon Beam Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-31Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-41Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-43Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-45

x THE PHYSICS AND TECHNOLOGY OF RADIATION THERAPY

Chapter 10 Central Axis Dose Distribution

10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-110.2 Percent Depth Dose (PDD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-410.3 Dependence of dm on Field Size and SSD . . . . . . . . . . . . . . . . . . . . . . 10-1010.4 Tissue-Air Ratio (TAR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-1110.5 Backscatter and Peak Scatter Factors. . . . . . . . . . . . . . . . . . . . . . . . . . 10-1310.6 Tissue-Phantom Ratio (TPR) and Tissue-Maximum Ratio (TMR) . . . . 10-1410.7 Equivalent Squares. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-1610.8 Linear Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-18Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-20Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-22Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-23

Chapter 11 Calibration of Megavoltage Photon Beams

11.1 Normalization Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-211.1.1 Normalization Conditions for Co-60 . . . . . . . . . . . . . . . . . . . . 11-311.1.2 Normalization Conditions for Linear Accelerators . . . . . . . . . . 11-3

11.2 Steps in Beam Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-411.3 Ion Chamber Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-511.4 Beam Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-811.5 The Task Group 51 Dose Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-911.6 Calibration Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-1011.7 An Example of TG-51 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-1111.8 Constancy Checks of Beam Calibration . . . . . . . . . . . . . . . . . . . . . . . . 11-12Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-14Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-16Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-18

Chapter 12 Calculation of Monitor Unit/Timer Settingfor Open Fields

12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-112.2 Normalization Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-312.3 Head Scatter and Phantom Scatter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-512.4 Dose Rate Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-8

12.4.1 Percent Depth Dose Calculations (SSD = SAD). . . . . . . . . . . . 12-812.4.2 Isocentric Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-1112.4.3 Dose Rate at an Arbitrary Distance . . . . . . . . . . . . . . . . . . . . . 12-1212.4.4 The Equivalence of PDD and TMR Calculations . . . . . . . . . . . 12-16


CONTENTS xi

Chapter 13 Shaped Fields

13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-113.2 Field Shaping Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-2

13.2.1 Asymmetric Jaws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-213.2.2 Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-313.2.3 Multileaf Collimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-6

13.3 Dose Rate Calculations for Shaped Fields: Symmetric Jaws,Central Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-1013.3.1 Approximate Methods for Estimating the Equivalent Square

of a Blocked Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-1313.3.2 Clarkson Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-17

13.4 Dose Rate Calculations for Shaped Fields at Points Awayfrom the Central Axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-22

13.5 Dose Rate Calculations with Asymmetric Jaws . . . . . . . . . . . . . . . . . . 13-2613.6 Dose Under a Blocked Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-28Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-31Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-33Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-36

Chapter 14 Dose Distributions in Two and Three Dimensions

14.1 Isodose Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-214.2 Skin Contour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-6

14.2.1 Isodose Shift Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-814.2.2 Effective SSD Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-1114.2.3 Ratio of TAR (rTAR) Method . . . . . . . . . . . . . . . . . . . . . . . . . 14-12

14.3 Parallel-Opposed Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-1414.3.1 Adding Isodose Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 14-1714.3.2 Beam Weighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-18

14.4 Wedges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-2014.4.1 Wedged Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-2414.4.2 Wedge Transmission Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-2414.4.3 Dose Rate Calculations with a Wedge Present . . . . . . . . . . . . . 14-27

14.5 Multiple Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-2814.6 Dose-Volume Specification and Reporting . . . . . . . . . . . . . . . . . . . . . . 14-3114.7 Evaluation of Patient Dose Distributions . . . . . . . . . . . . . . . . . . . . . . . 14-3414.8 Arc or Rotation Therapy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-4114.9 Surface Dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-4414.10 Bolus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-4614.11 Beam Spoilers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-4814.12 Tissue Compensators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-4814.13 Tissue Inhomogeneities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-5014.14 Field Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-58

xii THE PHYSICS AND TECHNOLOGY OF RADIATION THERAPY

14.15 Patient Positioning and Immobilization Devices . . . . . . . . . . . . . . . . . 14-67Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-71Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-74Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-78

Chapter 15 Electron Beam Dosimetry

15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-115.2 Electron Applicators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-515.3 Field Shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-615.4 Dose Rate Calculations for Electron Beams . . . . . . . . . . . . . . . . . . . . . 15-915.5 Internal Blocking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1415.6 Isodose Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1615.7 Inhomogeneities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1815.8 Field Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-21Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-22Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-25Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-26

Chapter 16 Brachytherapy

16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-116.2 Review of Radioactivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-216.3 Radioactive Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-316.4 Brachytherapy Applicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-716.5 Source Strength and Exposure Rate Constant . . . . . . . . . . . . . . . . . . . 16-1016.6 Dose Rate Calculations from Exposure Rate . . . . . . . . . . . . . . . . . . . . 16-1316.7 Specification of Source Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-1716.8 Task Group 43 Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-1816.9 Accumulated Dose from Temporary and Permanent Implants . . . . . . . 16-2016.10 Systems of Implant Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-21

16.10.1 A Point Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-2116.10.2 A Linear Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-2216.10.3 Planar and Volume Implants. . . . . . . . . . . . . . . . . . . . . . . . . . 16-24

16.11 Intracavitary Treatment of Cervical Cancer . . . . . . . . . . . . . . . . . . . . . 16-2916.12 Along and Away Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-3416.13 Localization of Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-3616.14 High Dose Rate Remote Afterloaders. . . . . . . . . . . . . . . . . . . . . . . . . . 16-36Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-41Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-44Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-45

CONTENTS xiii

Chapter 17 Radiation Protection

17.1 Dosimetric Quantities Used for Radiation Protection . . . . . . . . . . . . . . 17-317.2 Exposure of Individuals to Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . 17-517.3 Biological Effects of Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-8

17.3.1 Carcinogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-917.3.2 Risk to Fetus/Embryo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-1117.3.3 Genetic Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-14

17.4 Radiation Protection Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-1417.5 NRC Regulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-15

17.5.1 Annual Dose Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-1517.5.2 Medical License and General Requirements. . . . . . . . . . . . . . . 17-1717.5.3 Written Directives and Medical Events . . . . . . . . . . . . . . . . . . 17-1817.5.4 Examples of Events Reported to the NRC . . . . . . . . . . . . . . . . 17-2017.5.5 Radiation Protection for Brachytherapy Procedures . . . . . . . . . 17-2217.5.6 NRC Safety Precautions for Therapy Units . . . . . . . . . . . . . . . 17-24

17.6 Personnel Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-2717.7 Shipment and Receipt of Radioactive Packages . . . . . . . . . . . . . . . . . . 17-31

17.7.1 Package Labels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-3117.7.2 Receipt of Radioactive Packages (NRC Regulations) . . . . . . . . 17-32

17.8 Shielding Design for Linear Accelerators. . . . . . . . . . . . . . . . . . . . . . . 17-3217.8.1 Primary Barriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-3517.8.2 Secondary Barriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-3717.8.3 Neutrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-3917.8.4 The Entryway. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-3917.8.5 Radiation Protection Survey of a Linear Accelerator . . . . . . . . 17-40


Chapter 18 Physical Quality Assurance and Patient Safety

18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-118.2 Equipment Quality Assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-2

18.2.1 Linear Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-418.2.2 NRC Regulations Pertaining to QA . . . . . . . . . . . . . . . . . . . . . 18-1318.2.3 Dosimetry Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-15

18.3 Patient Quality Assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-1518.3.1 Physics Chart Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-1518.3.2 Weekly Physics Chart Checks . . . . . . . . . . . . . . . . . . . . . . . . . 18-1618.3.3 Portal Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-1718.3.4 In Vivo Dosimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-17

18.4 Starting New Treatment Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-2018.5 Mold Room Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-2118.6 Patient Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-21

xiv THE PHYSICS AND TECHNOLOGY OF RADIATION THERAPY

18.7 Radiation Therapy Accidents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-2218.7.1 A Linear Accelerator Calibration Error. . . . . . . . . . . . . . . . . . . 18-2218.7.2 An HDR Accident . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-2218.7.3 Malfunction 54 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-2318.7.4 Co-60 Overdose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-24


Chapter 19 Imaging in Radiation Therapy

19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-119.2 Digital Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-319.3 Conventional Simulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-719.4 Computed Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-10

19.4.1 Development of CT Scanners . . . . . . . . . . . . . . . . . . . . . . . . . . 19-1219.4.2 CT Image Reconstruction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-1919.4.3 CT Numbers and Hounsfield Numbers . . . . . . . . . . . . . . . . . . . 19-2119.4.4 Digitally Reconstructed Radiographs . . . . . . . . . . . . . . . . . . . . 19-2319.4.5 Virtual Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-2419.4.6 4D CT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-24

19.5 Magnetic Resonance Imaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-2719.6 Image Fusion/Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-3219.7 Ultrasound Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-3419.8 Functional/Metabolic Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-3619.9 Portal Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-39

19.9.1 Port Films. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-4019.9.2 Electronic Portal Imaging Devices . . . . . . . . . . . . . . . . . . . . . . 19-40

19.10 Image-Guided Radiation Therapy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-42Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-47Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-50Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-51

Chapter 20 Special Modalities in Radiation Therapy

20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-120.2 Intensity Modulation in Radiation Therapy . . . . . . . . . . . . . . . . . . . . . 20-1

20.2.1 IMRT Delivery Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-620.2.2 Inverse Treatment Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-1120.2.3 Inverse Planning Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-1820.2.4 Case Study: Prostate Cancer . . . . . . . . . . . . . . . . . . . . . . . . . . 20-2120.2.5 Aperture-Based Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 20-2220.2.6 Physics Plan Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-2220.2.7 Whole-Body Dose and Shielding . . . . . . . . . . . . . . . . . . . . . . . 20-25

CONTENTS xv

20.3 Stereotactic Radiosurgery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-2720.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-2720.3.2 Linac-Based Radiosurgery . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-3020.3.3 Gamma Knife® . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-3420.3.4 Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-3720.3.5 Treatment Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-3820.3.6 Dosimetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-4020.3.7 Quality Assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-40

20.4 Proton Radiotherapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-4120.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-4120.4.2 Potential Advantages of Protons. . . . . . . . . . . . . . . . . . . . . . . 20-4220.4.3 Proton Therapy Accelerators . . . . . . . . . . . . . . . . . . . . . . . . . 20-4420.4.4 Production and Selection of Different Energy Beams. . . . . . . 20-5120.4.5 Lateral Beam Spreading and Field Shaping with Protons . . . . 20-5220.4.6 Beam-Delivery/Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-5520.4.7 Dose Calculations and Treatment Planning

for Proton Therapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-5620.4.8 Dose Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-6120.4.9 Calibration of Proton Beams and Routine Quality

Assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-6320.4.10 Future Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-63


Appendix A – Board Certification Exams in Radiation Therapy . . . . . . A-1

Appendix B – Dosimetry Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-1

Appendix C – Mevalac Beam Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-1

Appendix D – Answers to Selected Problems . . . . . . . . . . . . . . . . . . . . . D-1

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I-1

xvi THE PHYSICS AND TECHNOLOGY OF RADIATION THERAPY

PrefaceThis book is the outgrowth of a course taught to residents in radiation oncology atWayne State University and at William Beaumont Hospital. Over the years the resi-dents have repeatedly urged that the lecture notes for the course be turned into abook. This is a result of frustration stemming from the lack of a text that is set at thecorrect mathematical level, is technically accurate, and pedagogically effective.

This book is aimed at the reader who has taken one year of college physics, per-haps years ago (and may not have been terribly thrilled about it). The reader may ormay not have taken college calculus or precalculus years ago and may only dimlyrecall natural logs and the exponential function.

There are a number of excellent texts on the physics of radiation therapy includ-ing those by Khan and Johns and Cunningham. We recommend these as good sec-ondary texts for those who wish to go beyond the basics. Both of these texts seem tobe a compromise between the needs of graduate students in medical physics and therest of the radiation therapy community. This book is specifically for the rest of theradiation therapy community. This includes radiation therapy technologists anddosimetrists as well as radiation oncologists; however, it may also be useful to thenovice physicist who is looking for a quick qualitative overview. Do not be misled,however; this is not a “watered down” text. Every effort has been made to makeexplanations clear and simple without oversimplifying. If you seek erudite and obfus-cating verbiage, find another text. To get the most out of this book we suggest thatyou “work” your way through it: follow along with pen in hand and work through theexample problems and derivations with us (see the quote, page vi).

We are mindful of the fact that people have professional exams that they muststudy for and pass. This book has been written with a close eye on the requirementsfor these exams—the ABR boards for physicians, the CMD exam for dosimetrists,and the ARRT for therapists. We make no apology to purists for this. If these examsare good exams, then they reflect what practitioners really need to know to be effec-tive clinicians. Teaching for the exam is simply teaching what people need to know.

It is one of the goals of this book to be interesting so that you will want to readit. We have attempted to accomplish this in two ways: by making the material asdirectly relevant to clinical activity as possible and by adding some interesting side-lights here and there, such as a brief discussion of atomic bombs, the discovery of xrays, and grand unified theories (GUTS) of particle physics, to name a few. You willhave to be the judge as to whether we have succeeded in this.

Whenever possible we have endeavored to explain where results come from andto emphasize principles. In some cases this means simple derivations, in other casesplausibility arguments. Otherwise one is left to blindly memorize facts and rules.Simple memorization leaves one lost when the circumstances change slightly. On the

xvii

other hand, we don’t want this book to be overly “theoretical.” For this reason wehave included the “clinical example” boxes and “rules of thumb” in the chapters thatare more theoretical.

There has not been any attempt to cover treatment planning. It is “beyond thescope of this book,” as they say. We recommend the excellent books by Bentel andKhan et al. We do however explain some of the basic principles that determine dosedistributions in patients. It is our opinion that the basic foundational material in thisbook should be covered first, before learning treatment planning.

A word about the use of mathematical symbols and equations. We know that therather extensive use of mathematical symbols may be foreign to our readers (unlessthey have majored in mathematics, physics, engineering, or Greek). We have endeav-ored to choose symbols very carefully for the many quantities referred to in this book.We have tried to make these symbols as simple as possible. As a result of the largenumber of quantities involved in the study of radiation therapy physics, there are sim-ply not enough Latin letters and we resort to Greek letters and or subscripts. We havetried to conform to standard usage where we believe it to be sensible. Unfortunatelythere are some symbols that are used for more than one quantity even in standardusage. The meaning of duplicate symbols is generally clear from the context.

Each chapter has a complete summary and a full problem set. Answers toselected problems may be found in appendix D. Clinically realistic dosimetry datafor a fictitious linear accelerator may be found in appendix C.

We have made every effort to provide accurate data and information; howeverthe information in this book should not be used for treating patients without firstconsulting a qualified medical physicist.

We welcome your comments and suggestions. We will try to answer e-mail ques-tions whenever possible.

Patrick N. McDermott, Ph.D.Email: [email protected]

Colin G. Orton, Ph.D.Email: [email protected]

xviii THE PHYSICS AND TECHNOLOGY OF RADIATION THERAPY

19 Imaging inRadiation Therapy

19.1 Introduction19.2 Digital Images19.3 Conventional Simulators19.4 Computed Tomography19.5 Magnetic Resonance Imaging19.6 Image Fusion/Registration19.7 Ultrasound Imaging19.8 Functional/Metabolic Imaging19.9 Portal Imaging19.10 Image-Guided Radiation TherapyChapter SummaryProblemsBibliography

19.1 IntroductionThe improvement in non-invasive imaging of the human body over thelast 35 years has been nothing short of astonishing.1 The imaging needsof radiation therapy are often quite different from those of diagnosticradiology and can be divided into two broad categories: imaging fortreatment planning and imaging for treatment verification. Both of thesecategories are complex and we can only address the main features here.

Imaging for treatment planning is used to define the gross tumorvolume and organs at risk and to select geometric parameters such asthe location of the isocenter and treatment beam angles. The imagingmodalities used for treatment planning can be divided into two cate-gories: conventional and three-dimensional. Conventional imaging

19-1

1 See Naked to the Bone: Medical Imaging in the Twentieth Century by B. Kevles, 1997.

includes general radiography and fluoroscopy. Conventional treatmentsimulators (see section 19.3) provide these capabilities. Conventionalimaging can be thought of as two-dimensional imaging in which three-dimensional anatomy is projected onto a plane. Plane film radiographsare “shadow pictures” or projection images. Three-dimensional imagingmodalities include CT (computed tomography), MRI (magnetic reso-nance imaging), ultrasound, SPECT (single photon emission computedtomography), and PET (positron emission tomography). These modali-ties provide true three-dimensional anatomical information and in thecase of SPECT and PET, metabolic information.

Plane film, fluoroscopy, and CT are based on x-rays as the imag-ing agent. MRI is based on nuclear magnetic resonance (NMR). Itinvolves “interrogating” the magnetic properties of atomic nuclei in amagnetic field. Radio frequency electromagnetic waves are used toaccomplish this. No ionizing radiation is employed in MRI. There is an“urban legend” regarding the name “magnetic resonance imaging.”The original name for this technique was nuclear magnetic resonance.As the public is so averse to anything with the word “nuclear” in it,the name was changed to MRI. Ultrasound (US) imaging is based onthe propagation and reflection properties of sound at tissue interfaces.PET imaging is based on the administration of a positron emitter andthe differential uptake of the radiopharmaceutical in different organsand tissues.

For treatment planning purposes it is often necessary to be able todiscriminate between various types of soft tissue. Ordinary or “plane”radiographs can distinguish between soft tissue and bone and betweensoft tissue and air, but not between different types of soft tissue. Gener-ally you cannot see tumors on plane films.

The three most widely used modalities for soft tissue imaging areCT, MRI, and ultrasound. For high spatial resolution and soft tissue dis-crimination MRI is unsurpassed (see Figure 19.1).

The imaging that we have described so far is anatomical imaging.Functional imaging such as PET and fMRI (functional MRI) displayphysiological activity such as glucose metabolism. This promises toplay an increasingly important role in the future of radiation therapy.

Traditionally, megavoltage imaging using the treatment beam hasbeen employed for treatment verification using either film or electronicportal imaging devices (EPIDs). EPIDs have now replaced film in mostclinics. A new development is image-guided radiation therapy (IGRT).In IGRT the patient is imaged on the treatment machine just prior totreatment. The location of the target is compared with the expectedlocation and the patient is moved to bring the target into alignment withits expected location. A variety of imaging modalities are in use forIGRT including on-board kVp imagers and ultrasound.

19-2 THE PHYSICS & TECHNOLOGY OF RADIATION THERAPY

19.2 Digital ImagesDigital images are images that can be stored in a computer in numer-ical form. CT and MRI produce digital images directly. Ordinaryradiographic film produces analog images. Film images can be “digi-tized” by scanning them with a film scanner such as the one shown inFigure 8.24 in chapter 8.

Electronic computers are fundamentally based on a large numberof switches. Physically these switches are transistors that reside onintegrated circuits (“chips”). A switch may be either “on” or “off.”There is no in-between state. An on or off state is like a “yes” or a “no”or like a 1 or 0. For this reason the natural number system for elec-tronic digital computers consists of the digits 0 and 1 only. This systemof numbers consisting of only two digits is called base 2 or binary. Ourcommonly used number system, the decimal system, is base 10. It con-sists of the digits 0, 1, 2, . . . , 9. The term “bit” is shorthand nomen-clature for a binary digit. It is either a 1 or a 0; it is the most elementaryunit of information.

Any base 10 number can be expressed as a binary number. Table19.1 shows the conversion from decimal to binary for the decimal num-bers 0 through 5.

A byte is 8 bits of information. An example is the 8-bit number11000010.

IMAGING IN RADIATION THERAPY 19-3

Figure 19.1: Side-by-side images of the same axial section made with CT (a) and MRI (b). The superiorsoft-tissue discrimination of MRI is evident. CT shows bone better than MRI. Note that itis conventional to always display the patient’s right on the left-hand side (patients areviewed from inferior to superior direction).

(a) (b)

Alphanumeric characters are the 26 letters of the alphabet (bothupper and lower case) plus the ten base ten digits 0, 1, . . . , 9 and spe-cial symbols such as $, #, etc. A byte can be used to represent a partic-ular alphanumeric character. There are 28 different ways to representa string of 8 ones and zeroes. Therefore there are 28 � 256 possiblecharacters a byte can represent. This is the reason that the original PCcharacter set contains 256 characters.

There are some useful prefixes in computer science that are a littledifferent (we won’t make a bad pun and say “a bit different”) than definedin Table 2.2. A kilobyte is 210 � 1024 bytes. A megabyte (MB) is 220 �1,048,576 bytes. A gigabyte is 230 bytes, etc. As an example, a 100 GBstorage disk will hold approximately 1.074�1011 bytes of data.

There is a standard binary coding scheme for alphanumeric charac-ters, the American Standard Code for Information Interchange, known asASCII (pronounced ass-key) for short. There are 128 standard charactersand each character is represented by an 8-bit (one byte) number. Forexample a “W” is represented as the 8-bit binary number 01010111.ASCII is the lingua franca of the computer world. Most computers rec-ognize ASCII. A page of ASCII text is about 2 kbytes. A more recentindustry standard is Unicode, which is used to represent about 100,000different text characters in use throughout the world.

Digital images are divided up into an array or grid of picture elementscalled pixels. The pixel size influences the spatial resolution of an image.The larger the pixel size the poorer the resolution (see Figure 19.2). For aspecific image, smaller pixel size means that more pixels are necessaryto depict the entire image. More pixels provide higher spatial resolution.There is a cost however; more pixels mean more storage space required.Radiological images are generally either 512�512 pixels or 1024�1024pixels. This is crude compared to the resolution available in consumerdigital cameras.2


Decimal (base 10) Binary (base 2)

0 0

1 1

2 10 � 1 � 21 � 0 � 20

3 11 � 1 � 21 � 1 � 20

4 100 � 1 � 22 � 0 � 21 � 0 � 20

5 101 � 1 � 22 � 0 � 21 � 1 � 20

Table 19.1: Binary Numbers

2 At the time of this writing, 10 megapixel cameras are common. This corresponds to an image of3888�2592 pixels.


Figure 19.2: A series of four images with different numbers of pixels. The first image on the left has345�487 pixels. The second image is approximately 30�45 pixels. The third is approxi-mately 16�22 and the fourth is 8�11. The larger the number of pixels, the greater thespatial resolution.

The field of view of a fluoroscopic unit is 9 in. (23 cm) across.Images are acquired in a 512�512 pixel format.

What is the pixel size and what is the size of the smallest objectthat can be resolved?

The pixel size is 23 cm/512 � 0.45 mm per pixel. Any object thatis about 0.5 mm or smaller will be difficult to discern.

Example 19.1

Images that we might normally describe as “black and white”(such as in old movies) actually have many shades of gray. In a “grayscale” image, each pixel is assigned a number that represents a shadeof gray or a gray level. This is called the gray scale. In a color imageeach pixel is assigned a number that represents a color. The numericalvalues assigned to a pixel are binary. An example is an 8-bit gray scalewhich has 28 � 256 shades of gray. The number of shades of gray inan image affects the contrast resolution of the image. This is illus-trated in Figure 19.3.

For three-dimensional imaging purposes the region of interest in apatient is divided up into a large number of small volume elements orvoxels. The goal of three-dimensional imaging is to determine the valueof some quantity characterizing the tissue in each one of the voxels.This value is presumed to be constant within each of the small voxels.The image can only be displayed however in two dimensions as either asectional image or a projection image.3 A sectional image is oftendescribed as a “slice.” A slice may be as little as one voxel thick. Thereare three principal types of sectional images. An axial or transverseslice divides a patient into two halves, a superior half and inferior half.


Figure 19.3: Three images having different gray-scale levels. The image on the left has an 8-bit grayscale. The middle image has a 4-bit gray scale. The image on the right is a 2-bit image:there are only two shades—black and white. This image is true black and white.

A CT image is 512�512 pixels and has 16-bit pixel values (only 12bits are used for the gray scale). How many bytes are required tostore this image?

The total number of bits � 512�512�16 � 4,194,304 bits. Thenumber of bytes � 4,194,304/8 � 524,288 and 524,288/1024 �512 kbytes. The file will be slightly larger because of the presenceof an image “header” containing information about the image(patient name, date, etc.).

Example 19.2

3 This paragraph follows the discussion in Radiation Oncology: A Physicist’s Eye View by M. Goitein,2008.

A coronal section divides a patient into an anterior half and a posteriorhalf and a sagittal section divides a patient into left and right halves. Aprojection image is one in which each pixel represents a transmissionvalue through all tissue traversed between the source and image plane.The prime example is an ordinary radiograph.

Standardization of image data files is a very critical issue. It isimportant to be able to seamlessly transfer images between imagingdevices, treatment planning systems, record and verify systems, etc.Most manufacturers now comply with the DICOM (Digital Imaging andCommunication in Medicine) standard. An extension of this standard iscalled DICOM-RT and includes specific provisions for radiation ther-apy. Radiological images are often stored and transferred within aPicture Archiving and Communication System (PACS). This replaceshardcopy film and allows remote access. A PACS consists of servers forimage storage that are connected to client viewing stations via a net-work system. A PACS enables easy access to radiological images any-where throughout a hospital or hospital system.

19.3 Conventional SimulatorsThere are two types of simulators used for radiation therapy: conven-tional and CT. Both types of simulator are intended to provide informa-tion necessary for the planning and treatment of patients. A conventionalsimulator is a device which mechanically simulates the behavior of alinac or Co-60 unit (see Figure 19.4). There is a gantry, which canrotate, and a couch, which may be identical to a linac or Co-60 treat-ment couch. All of the motions that are possible on a linac are dupli-cated in a conventional simulator. In addition, the source-axis distance(SAD) can be set on a simulator. Simulators also have a block trayholder. The tray slot must be at the same distance from the x-ray sourceas the tray on the linac. In addition, a conventional simulator is capableof kV (diagnostic quality) imaging including fluoroscopy. This isneeded to assist in planning patient treatments. Linear accelerators arenot capable of diagnostic quality images or fluoroscopy. This is themajor reason a simulator is used rather than a linac to plan a patient’streatment. Fluoroscopy allows adjustment of the beam position underreal time conditions. Conventional simulators are likely to disappearover the next ten years in favor of CT simulators.

A simulator room is divided into two areas: a control console areaand an area containing the simulator. The simulator consists of a con-sole, a gantry, a gantry stand, and an x-ray generator. The simulatorroom is the place where most of the information necessary to plan andto treat a patient is gathered. Once simulation data are collected (films,gantry angles, etc.), it will be passed along to a dosimetrist for treatmentplanning on a treatment planning computer system. The simulator roomhas wall-mounted lasers for patient positioning just like a treatment


room (see Figure 18.2 in chapter 18). Treatment aids, such as immobi-lizing devices, are usually fabricated during a patient’s simulationappointment. The patient is usually marked or tattooed in the simulatorroom.

The simulator has a diagnostic x-ray tube in the head, which is usedfor fluoroscopy and plane film imaging. Focal spot sizes range from 0.4to 0.6 mm for the small spot and 1.0 to 1.2 mm for the large spot. Thesimulator has a grid, a film cassette holder, and an image intensifier (II)for fluoroscopic imaging. Newer simulators have digital flat-panel,solid-state detectors instead of an II. Fluoroscopy is activated with theuse of a foot pedal. The II can be moved up and down, from side to side,and in and out. The presence of the II constrains gantry and tablemotion. A collision avoidance system is built into the II so that it can-not hit the treatment couch.

The II is a large, evacuated tube with a cesium iodide fluorescentscreen at one end that converts x-rays to light (see Figure 19.5). Thelight from this screen strikes a photocathode, which in turn emits low-


Figure 19.4: A conventional simulator is designed to be mechanically like a linac in that it mimics themotion of a linac. The exception is that the SAD can be changed (B). The head houses adiagnostic x-ray tube and at the other end of the gantry there is a grid, film cassetteholder (L), and an image intensifier (M) for fluoroscopy. The image intensifier can bemoved laterally (D and E) and up and down (F). (Reproduced from Radiotherapy Physicsin Practice, J. R. Williams and D. I. Thwaites (eds.), Fig. 7.3, p. 125, © 2000 by permissionof Oxford University Press.)

energy photoelectrons. In this way the x-ray image is converted to anelectronic image. The electrons are accelerated and focused by a highvoltage (up to 30 kV) between the ends of the tube. At the end of thetube the electrons strike a small output fluorescent screen, producing avisible light image of high brightness. The brightness gain is due to twofactors: the energy acquired by the accelerated electrons and the reduc-tion in the diameter (minification) of the image. The image is directedinto a camera through a mirror tilted at a 45° angle. The image isviewed on a TV monitor in the control console area. Many simulatorshave “last image hold,” which enables continued viewing of an imageafter the x-ray beam turns off. The brightness level is set by the auto-matic brightness control (ABC). A photocell located between the II andthe camera sends a signal back to the generator to adjust the kVp ormA. As the patient is moved with respect to the II, the ABC maintainsthe proper brightness level.

When planning patient treatment it is necessary to select gantry, col-limator, and couch (pedestal) angles for each beam or treatment field. Inaddition, the location of the isocenter must be chosen with respect to


Figure 19.5: An image intensifier (see L and M in Figure 19.4) is a large evacuated tube that containsa fluorescent cesium iodide input screen. The CsI input screen converts x-rays to visiblelight, which in turn strikes the photocathode and generates electrons. The electrons areaccelerated and focused. When the electrons strike the output screen, they produce asmaller and much brighter image.

the patient. Simulators have four independent delineator wires whichtake the place of linac independent jaws and cast a shadow which showswhere the jaws will be positioned on the linac. This allows the physicianto view adjacent anatomical structures. Radiographic contrast agentsmay be used in the bladder, etc. A graticule scale projected onto the filmshows the beam central axis and graduated scale (see Figure 19.6).

The control console is used to set the radiographic technique: kVp,mA, and time. Modern generators produce high-frequency dc with lowripple (see chapter 5, section 5.2). The control console is behind a bar-rier which is shielded against kV scatter x-rays. There may be an inter-lock on the exterior door so that the x-ray beam is shut off if the door isopened. The simulator and patient can be viewed from the control con-sole, usually through a leaded glass window. The control console canalso be used to remotely set the gantry angle, collimator angle, delin-eator wires, and position of the II. The control area also has the videodisplay monitor for fluoroscopy.

19.4 Computed TomographyComputed tomography (CT) was developed by G. N. Hounsfield andA. M. Cormack. The first commercially available unit was introducedby EMI Ltd., in 1970. This company is perhaps best known for firstrecording the Beatles! Hounsfield and Cormack won the Nobel Prize for


Figure 19.6: A simulation film of a patient’s pelvis (a) next to a 6 MV localization film (b). The qualityof the simulation film is far superior to the localization film. The delineator wires areshown on the “sim” film. A graticule on the sim film shows lateral distance as measuredat isocenter. The wires are set for a 10�10 cm2 field. The dark central area on the local-ization film is the treatment field.

(a) (b)

Medicine in 1979. CT was one of the most significant developments inmedical imaging in the twentieth century. What’s the breakthrough?

(1) Three-dimensional imaging.(2) Soft tissue discrimination.

Herein lies the power of CT.

As shown in Figure 19.7 the patient lies on a table, which can moveup and into the aperture (sometimes called the bore). The inferior andsuperior scan limits are selected first by performing a transmission scan(also called a topogram, scout, or surview). For this purpose the patientis moved through the bore while the x-ray tube is on but stationary (notrotating). Based on the image formed by this procedure, the operatorthen selects the inferior and superior limits of the scan. During the scanitself the x-ray tube rotates around the patient. The x-rays pass throughthe patient and are detected by a detector array opposite the tube and


Figure 19.7: The mechanical motions of a CT scanner. The table is moved into the bore. An x-ray tubeinside the gantry rotates around the patient. A detector array registers the x-ray inten-sity passing through the patient. The detector signals are fed to a computer, whichthen “reconstructs” a series of axial images (“slices”) of the patient. (Reproduced fromRadiotherapy Physics in Practice, J. R. Williams and D. I. Thwaites (eds.), Fig. 7.8, p. 135,© 2000 by permission of Oxford University Press.)

converted into electrical signals. The signals from the array are fed intoa computer, which then “reconstructs” an axial slice or tomogram (seeFigure 19.1) of the patient. This is quite different from the “shadow”picture formed by plane radiography. As the table moves further into thebore, successive slices in the inferior direction are reconstructed. Theseslices can be stacked to form a three-dimensional image of the patient.This provides a digital model of the patient, including both geometricdata (location of skin surface, tumor, and organs at risk) and composi-tion data (linear attenuation coefficient). This digital model is exportedto a treatment planning system.

CT images are the primary imaging modality used for radiationtherapy treatment planning purposes. There are three reasons for this:CT images are spatially accurate. They are not subject to spatial or geo-metric distortions. An accurate model of the patient is necessary foraccurate dose calculations, both spatially and in terms of composition(i.e., electron density). The second reason is that the spatial resolutionof CT is relatively high (compared to PET, for example). The third rea-son is that electron density data can be derived from the CT number(CT#), provided that a calibration curve is available (see section 19.4.3).MRI can suffer from spatial distortion, and it does not provide electrondensity data.

CT images represent a “virtual” patient. CT units are either diag-nostic scanners or speciality scanners, called CT simulators, sold specif-ically for radiation therapy treatment planning. The advent of CTsimulators and the use of “virtual simulation” may signal the end ofconventional simulators. Virtual simulation involves the use of CTimages along with software to “virtually” simulate and plan treatment.The role that CT plays in treatment planning is twofold:

(1) Contour data: provides true 3-D data on spatial location of skin,tumor, normal organs and tissues.

(2) Electron density: recall that Compton scattering is the dominantphoton interaction at megavoltage therapy energies—dependsprimarily on the electron density (electrons/cm3) ⇒ inhomo-geneity corrections depending on electron density.

19.4.1 Development of CT scanners

Early model CT scanners acquired a single axial slice at one time withthe table immobile during tube rotation. The x-ray tube generates a fanbeam of x-rays that rotates around the patient. The table is thenadvanced to acquire the next slice. In this way contiguous axial slicesare generated. In the early 1990s spiral scanners were developed inwhich the table moves continuously while the x-ray beam remains on,


tracing out a helical path around the patient. At about the same time,multi-slice scanners were introduced. These scanners are capable ofacquiring multiple slices simultaneously. We will discuss each of theseimportant developments below.

We begin with a discussion of the development of axial (non-spiral),single slice scanners. These scanners have evolved through four gener-ations as shown in Figure 19.8. The first generation scanners used a pen-cil beam (Figure 19.8a) and a single detector. Both the x-ray tube andthe detector first moved horizontally (translate) through 180 positionsand then the x-ray tube and detector rotated 1°. This translate-rotateprocess was repeated until sufficient projections were obtained to forman image. It is not surprising that scan times were long, about 5 minutesfor a single axial slice. Second-generation scanners (Figure 19.8b) usedan x-ray fan beam and a multiple linear detector array. These scannersalso operated in a translate-rotate mode. The multiple detectorsincreased speed considerably, but it still took as long as 20 seconds toimage a single slice. Third-generation scanners use a fan beam and adetector array containing at least 30 elements (Figure 19.8c). Transla-tion is no longer necessary, and both the tube and detector rotate. Scantimes are as low as 1 second for an axial slice. In a third-generationscanner, each detector element images a particular annulus of thepatient’s anatomy. If an element is not functioning properly, a “ring”artifact may result. In a fourth-generation scanner (Figure 19.8d) thedetectors form a ring completely surrounding the patient and thereforeonly the x-ray tube rotates. Most scanners sold today are actually third-generation scanners.

The x-ray detectors are either xenon gas ionization detectors, usedin some third-generation scanners, or solid-state scintillation crystalsused in third- and fourth-generation scanners. The thinnest slice thick-ness is determined by detector collimation and reconstruction parame-ters. Various slice thickness settings are possible: 1, 2, 5, and 10 mm arecommon. Spatial resolution can be as good as 0.6 mm in the axial plane.

Single-slice scanners have two major disadvantages. First, they arevery slow, and second they suffer from poor resolution in the longitudi-nal direction. A non-spiral set of single-slice CT scans for treatmentplanning using a third- or fourth-generation scanner can take as long as45 minutes. This is time-consuming for staff, and it is difficult for somepatients to remain in immobilization devices this long. Practical valuesof the slice thickness are relatively large. The resolution in the axialplane of a CT image is typically about 1 mm. It is not uncommon withold scanners to use a slice thickness of 5 mm or even 10 mm. The slicesare then stacked to form what could be described as a “pseudo 3-D”image. Because the resolution in the longitudinal direction is consider-ably poorer than in the axial plane, any object or boundary within agiven slice will be imaged, but its location within the slice will be



Figure 19.8: The four generations of CT units described in the text. (a) is a first generation unit, (b) issecond generation; (c) and (d) are third and fourth generations. Most CT units sold todayare third generation. (Reproduced from “CT Basics” by D. Cody in The Physics and Appli-cations of PET/CT Imaging, Figs. 1 and 2, pp. 30, 32. © 2008, with permission from Amer-ican Association of Physicists in Medicine (AAPM); previously printed in “ComputedTomography” by T. G. Flohr, D. D. Cody, and C. H. McCullough in Advances in MedicalPhysics: 2006, A. B. Wolbarst, R. G. Zamenhof, and W. R. Hendee (eds.), Figs. 3-4a/b, p. 63,© 2006, Medical Physics Publishing.)

unknown. This is sometimes called “volume averaging.” This impliesthat the location of anatomical boundaries is uncertain by an amountapproximately equal to the slice width. A 10-mm uncertainty in thesuperior/inferior direction may be unacceptable for highly conformalradiation therapy. In addition, digitally reconstructed radiographs(DRRs, see section 19.4.4) suffer from poor quality when the slicethickness is large.

New CT scanners are now helical (sometimes called spiral) scan-ners. These were introduced in the early 1990s. A non-spiral scan willbe referred to as an axial or sequential scan. Modern CT scanners canacquire images in either axial or spiral mode. Spiral scanners are thirdgeneration and as such both the tube and detector rotate. Electricalcables run both to and from the tube and the detector, carrying powerand data. In an axial scan the x-ray tube rotates as much as 360° aroundthe patient.

If rotation in an axial scanner were to continue in the same directionpast 360°, the cables would become increasingly wound or twisted.Therefore tube rotation must stop to avoid winding up cables. Duringthis time interval, the table is moved (indexed) further into the bore byan amount that is usually equal to the slice thickness and then the nextslice is acquired. Spiral CT is based on a continuous rotation of thex-ray tube as the patient is translated through the scanning aperture.Spiral scans eliminate the dead time associated with table motion. Inthis way it is possible to obtain up to 40 slices in a single breath hold.This reduces motion artifacts. Spiral CT has become possible throughthe introduction of “slip-ring” technology, which avoids the problem ofcable winding. The faster the tube can rotate, the more rapidly a scancan be completed. CT units are now available in which the tube canrotate through 360° in as little as 0.3 seconds. This places severe cool-ing demands on the x-ray tube and housing. These tubes must be capa-ble of handling a heavy heat load. They are therefore expensive, over$100,000. Oil is pumped through the tube housing and circulatedthrough a radiator. The rapid rotation requires the gantry to be spin bal-anced like an automobile tire.

Newer CT units are capable of multiple-slice scanning (seeFigure 19.9). These units can acquire more than a single slice simulta-neously. There are units that can acquire up to 64 slices at one time.These use multiple rows of detectors extending along the longitudinaldirection (z-axis, see Figures 19.7 and 19.9). The signals can be com-bined from adjacent elements to form slice thicknesses that are multi-ples of the size of a single detector element. The detector elements oftenhave varying width—smaller near z � 0. The total scan thickness in asingle rotation is related to the entire detector. The x-ray beam is now acone beam instead of a fan beam. Multi-slice units are third-generationscanners. The advantages of multi-slice scanning are faster acquisitiontime, reduced tube loading, the option of respiratory gating or sorting,


thinner slices, and greater volume coverage on a single tube rotation.Slice thicknesses of as little as 0.5 mm are feasible. This is true 3-Dimaging—the resolution in the z-direction is as good as the resolution inthe axial plane. Multi-planar reconstruction becomes a useful option; theresolution in coronal and sagittal planes is as good as in an axial plane.

There are some disadvantages of multiple slice scanning. The use ofa cone beam as opposed to a fan beam leads to increased scatter in thepatient and to the detector. To maintain image quality, scattered photonsare partially eliminated by using radiopaque separators (septa) betweendetector elements in the z-direction. This arrangement acts like a grid ina film cassette to eliminate image degradation due to scatter radiation(see chapter 4, section 4.4). The dose is higher for a multi-slice scancompared to an axial scan of like quality. This is due in part to increasedscatter in the patient from the large cone beam and decreased efficiencybecause of the presence of the septa between detector rows.

Each patient may have hundreds or up to perhaps one thousandimages (4D CT). As an example of data storage requirements, suppose100 patients are under treatment at a given time. Let us assume thatthere are 150 images per patient and each image is 512�512 pixels.Each pixel is 2 bytes (actual gray scale is 12 or 14 bits, they do not use


Figure 19.9: A multi-slice CT scanner showing the detector array and the cone beam diverging in thelongitudinal direction. A single-slice scanner would have a very narrow (in the longitudi-nal direction) fan beam whereas a multi-slice scanner has a cone beam. In this illustrationthe collimator has been set to produce a 16-slice scan; each slice is 0.75 mm thick (alldimensions measured at the isocenter). The largest total scan thickness for this scanner is16�0.75 � 8�1.5 � 24 mm.

the full 16 bits). This requires 512�512�2�150�100 � 7.3 GB stor-age just for current patients.

Reconstruction of images from a spiral scan is affected by the dis-tance that the table moves in one revolution of the x-ray tube and by thebeam thickness. The quantity pitch has been defined to describe this.With the introduction of multi-slice scanners the definition of pitch hasbeen refined so that it is relevant to both axial and multi-slice scans:

(19.1)

For a single slice axial scanner T� is the beam thickness as determinedby the x-ray collimator in millimeters. For a multi-slice scanner T� isthe total length of the tissue irradiated in millimeters (the length cov-ered by the beam in Figure 19.9).

The pitch has a direct impact on patient dose and image quality.When P < 1 (see Figure 19.10) there is an improvement in image qual-ity, but the dose is increased because of overlapping helical slices. WhenP > 1, less time is required for the scan, but not all regions are fully sam-pled; some z interpolation may be necessary resulting in a loss of resolu-tion along the z-axis. The pitch values for one commercially availableCT simulator range from 0.07 to 1.7 (for 4D CT, see section 19.4.6).

P =( )

′Table travel per rotation mm

T


Figure 19.10: A side view of a four-slice scan. In the top diagram the pitch is 0.75. This means that thetable travels 3/4 of the beam width (i.e., three channels) in one rotation. This causesdetectors 1 and 4 to overlap. When the pitch � 1.5 (bottom diagram), there is an under-lap and there is a gap in the coverage. [Reprinted from The Modern Technology of Radi-ation Oncology, vol. 2, J. Van Dyk (ed.), Fig 2.4, p. 38, © 2005; previously adapted andprinted in “McCullough, C. H., and F. E. Zink, “Performance evaluation of a multi-slice CTsystem,” Med Phys 26:2223–2230, © 1999 with permission from American Association ofPhysicists in Medicine (AAPM).]

Some radiation therapy departments do not have a dedicated CTunit. There are special considerations when using a diagnostic radiologydepartment CT unit for RT planning. The size of the bore is an impor-tant factor. Diagnostic CT scanners generally have a bore diameter of70 cm. This can be too small for RT for two reasons. The first reasonhas to do with patient immobilization and positioning devices; the sec-ond has to do with the size of the “scanned field of view.” The primeexample of the first reason is breast treatment where the patient is oftenlying on a breast board with her arm extended (see Figure 19.11). In thiscase, the patient may not fit through the bore. It is important thatpatients be scanned in the same position in which they will receivetreatment so that there is no distortion in patient geometry. For accuratetreatment planning, patient position must be identical during CT scanand treatment. Immobilization devices such as breast boards, alpha cra-dles, etc., may not fit through the bore. CT units cannot image over theentire bore aperture. The imaging size is specified by the scanned fieldof view. This must be large enough to encompass a patient’s skin sur-face completely. The treatment planning system needs complete infor-mation about the location of the patient’s skin surface to calculatetreatment depths accurately. CT scanners with bore sizes up to 90 cmare now on the market for radiation therapy planning purposes.

The couch top of diagnostic CT units is concave. For RT purposesthe couch top must be flat like the treatment couch, otherwise patientanatomy will be distorted. Couch inserts are available to make thecouch top flat. In fact, a simple board will suffice provided that it isplaced level, does not flex, and does not interfere with imaging.


Figure 19.11: A patient undergoing simulation for a breast treatment. The patient is lying on a breastboard. Note the position of her arm. This requires a large bore size for CT imaging.(Courtesy of Philips Healthcare, Andover, MA)

For radiation therapy, external lasers are needed for patient position-ing and marking. Diagnostic CT units only have internal gantry lasers.The internal lasers show the location of the scan plane. The externallasers are mounted outside the gantry. A set of lateral lasers is mountedeither on the floor or on the walls. These project perpendicular linesdefining coronal and axial planes, usually 50 cm inferior to the scanningplane (assuming patient goes in head first). An overhead laser projects asagittal fan beam perpendicular to the scan plane. This laser is some-times mobile, as it is not possible to move the CT couch laterally.

19.4.2 CT Image Reconstruction

The goal of image reconstruction is to use transmitted x-ray intensityinformation to determine the µ value for each volume element (called avoxel). The value of µ is then used to construct a gray-scale map, whichcan be portrayed as an image. The process is described in this and thefollowing section. A simple heuristic explanation follows.

In Figure 19.12 we consider the most elementary “patient” possible,one consisting of a single voxel of known side length x. A single x-rayprojection is used. A known intensity, I0, is incident on the voxel. Thetransmitted intensity, I, is measured by the detector (see Figure 19.8A).The relationship between the incident intensity and the transmitted inten-sity is I � I0e

–µx (see chapter 5, section 5.5). In this equation the knownquantities are I0, I, and x. Therefore we can solve for the one unknown µ.

Now let us consider a slightly more realistic example: a patient con-sisting of two voxels, as shown in Figure 19.13. We again use a singlex-ray projection. The relationship between the transmitted intensity and

the incident intensity is where I0, I, and x are known andµ1 and µ2 are unknown. In this case, we have a single equation in twounknowns and we cannot solve for µ1 and µ2 without more projections.

I I e x= − +( )0

1 2µ µ ,


Figure 19.12: A “patient” consisting of a single voxel.

Let us now consider a patient consisting of four voxels. We will usefour x-ray projections, as shown in Figure 19.14. We have the followingrelationships between the incident and transmitted intensities:

(19.2)


Figure 19.13: A “patient” consisting of two voxels.

Figure 19.14: A “patient” consisting of four voxels. Four x-ray projections are used.

I I e

I I e

I I e

x

x

1 0

2 0

3 0

1 2

3 4

2 4

=

=

=

− +( )

− +( )

− +(

µ µ

µ µ

µ µ ))

− +( )=

x

xI I e4 01 3µ µ .

We have four equations in the four unknowns µ1, µ2, µ3, and µ4.These equations can be solved for the unknowns.

In general, a patient consists of a large number of voxels n. Theillustration above has shown that provided there are enough projections,it is possible to solve for µ1, µ2, . . . , µn; that is, to find the µ value foreach voxel. In practice, we are faced with the mathematical task of solv-ing n equations in n unknowns where the value of n may be quite large.Sophisticated methods are used such as: 2-D Fourier transforms or“filtered backprojection.” In this way one obtains three-dimensionalinformation about the object imaged. This is called image reconstruction(recon). The calculations are carried out on a specialized computer inalmost “real time.” In the next section we discuss the problem of usingthe µ values to form an image.

19.4.3 CT Numbers and Hounsfield Units

Each pixel in a CT image requires a numerical gray-scale value for dis-play. The values of µ are converted to CT# or CT pixel value. These aresometimes known as Hounsfield units:

(19.3)

where µt is the linear attenuation coefficient of the tissue in a particularvoxel (for a given beam quality) and µw is the linear attenuation coeffi-cient for water. Hounsfield units have no dimensions. For airand therefore CT# � �1000 HU. For water µt � µw and thereforeCT# � 0 HU. The value of the CT# for dense bone depends on the kVpof the CT. At 100 kVp, µw � 0.206 cm–1 and µbone � 0.528 cm–1, thereforeCT# � 1000(0.528 � 0.206)/0.206 � �1560 HU. Most CT units have aCT# number range between �1000 HU and �3000 HU. High-densitymetal clips or prosthetic devices may have CT# approaching �3000 HU.

One HU represents a difference of 0.1% in attenuation coefficientwith respect to water. Most CT units have a noise error of �5 HU. Thisallows discrimination at the level of �0.5% in µt, enabling good con-trast resolution. This sensitivity is what makes CT useful for soft tissueimaging.

CT images are usually 512�512 pixels. CT numbers may span therange from �1000 HU to �3000 HU. There are therefore 4000 possiblevalues associated with each pixel. A 2-byte number associated witheach pixel can accommodate this as 216 � 6.6�104. Storage require-ments are therefore 512�512�2 bytes � 0.5 MB for each slice. CTnumbers must be converted into a gray level for display. The number ofshades of gray that can be perceived by the human eye is at most 256.

CT # ,=−

1000µ µ

µt w

w


µt ; 0 1cm−

One could assign 4000/256 � 16 HU to the same shade of gray, but thiswould compress the scale and we would lose information. Instead, oneshould only throw away information that is not needed. This is accom-plished by the use of a “window” and “leveling” system. A CT# is cho-sen that corresponds roughly with the average CT# in the region ofinterest. This value is called the “level” or center. A “window” width ischosen: for example, 128 shades below the center and 128 shades abovethe center. Pixels within the window are assigned gray-scale valuesbetween 0 and 255. Pixels below the window are set to black and pixelsabove the window are set to white. The window and level are chosen toobtain the required brightness and contrast for the type of tissue to beexamined. Reducing the size of the window increases contrast. Chang-ing the level allows inspection of a different range of CT numberswithin the window. As an example of this process, suppose that thelevel chosen is 200 HU and the window is 500. In this case CT numbersless than 200 � 500/2 � �50 are displayed as black and CT numbersabove 200 � 500/2 � 450 are displayed as white. One can adjust thewindow and level to obtain the desired brightness and contrast. Thisprocedure is followed whenever CT images are examined.

For treatment planning with inhomogeneity corrections (see chapter 14,section 14.13), it is necessary to convert Hounsfield units to electrondensity (electrons/cm3) by using a calibration curve. These curves are“bilinear” (see Figure 19.15). Calibration curves may be particular tothe scanner and the kVp used. They are obtained by scanning a special


Figure 19.15: The relative electron density as a function of CT# for a representative CT scanner. Sometissues are heterogeneous and it is therefore not possible to assign a single unique CT#.This curve displays a typical bilinear character.

phantom containing about a dozen inserts with various known electrondensities. An average CT number is measured for each insert and the elec-tron density can then be plotted versus CT number as in Figure 19.15.The calibration curve is used by the treatment planning system to makeinhomogeneity corrections.

High-density materials such as metal prosthetic implants, dentalfillings, etc., may lead to streak artifacts. These streaks may have veryhigh CT numbers. These high CT numbers are translated into high elec-tron densities. Such images must be used with care if inhomogeneitycorrections are turned “on” in the treatment planning system.

19.4.4 Digitally Reconstructed Radiographs

A plane film radiograph such as produced with a conventional simulatorprovides a beam’s-eye view but not 3-D information. CT provides axialslices but not a beam’s-eye view. The data contained in the CT recordhave information on the linear attenuation coefficient of each voxel.From these data it is possible to mathematically reconstruct a beam’s-eye view image for any treatment port. This is known as a digitallyreconstructed radiograph (DRR) because it is constructed from the dig-ital CT data. A DRR is like a simulated radiograph and can be used likean ordinary simulation film for comparison with port films. An exampleis shown in Figure 19.16. The DRR is constructed by considering raylines that emanate or diverge from the presumed source (e.g., the targetof a linac) and strike an imaging plane a chosen distance away. The


Figure 19.16: A beam’s-eye view DRR for a lateral whole-brain irradiation field. The MLC leaf positionsfor blocking are superimposed.

value of any image pixel is related to the transmission of the associatedray line through the patient. The magnification of a DRR can be speci-fied and various other image parameters can be easily manipulatedbecause of the digital nature of these images. For example, it is possi-ble to emphasize bone. DRR spatial resolution is improved by smallerslice thickness for the CT scan.

19.4.5 Virtual Simulation

The images acquired during a CT examination contain three-dimen-sional information about the patient’s anatomy. These images can beused in conjunction with computer software to perform a virtual patientsimulation immediately following CT image acquisition. The virtualsimulation software mimics the mechanical motion of the linac. Thisallows beam’s-eye view display for various gantry, collimator, andpedestal angles. The virtual simulation is used to define the treatmentisocenter. The patient can then be marked with tattoos before getting offthe CT couch. This often involves a set of lateral marks and an anterioror posterior mark. A system is necessary to ensure that the patient is inthe same position on the treatment table as during the CT scan. Lasersare used to locate the spot where the skin marks are placed. The simu-lation software indicates the necessary couch position for laser marking.Radiopaque BBs are sometimes placed over the marks. These will bevisible in the CT images and can be used to establish a coordinate sys-tem. As CT couches cannot be moved laterally, CT simulators have amoveable overhead sagittal laser. The sagittal fan beam is moved later-ally to indicate the correct position of the isocenter on the patient’s skin.

19.4.6 4D CT

The term “4D CT” refers to three spatial dimensions plus a time dimen-sion. This is used to track respiratory motion. Let us first consider theeffects of motion on CT images.

Refer to Figure 19.17. We imagine a spherical object in a patient’s lung.This object is moving up and down sinusoidally with the patient’s respi-ration. This object is shown in the figure (coronal view) at various timesthroughout two respiratory cycles. These snapshots in time are labeledwith numbers 1 through 11. For simplicity we assume pure axial scans(no helical scan). The first axial scan shows the very top of the sphere. Aside view of the axial scan slice is shown on the left in Figure 19.17. Thetop of the sphere is evident in this slice. The table is then indexed for thesecond axial scan, but by this time the sphere has moved out of the scanplane and does not show up on the axial slice labeled 2. The couch con-


tinues to move inward acquiring successive scans. A side view of eachaxial scan is shown at the bottom left. These can be stacked up to showa coronal image of the object (bottom right). The shape of the image ofthe object is clearly distorted. Figure 19.18 shows the respiratorymotion distortion of a patient’s lung tumor.

There are two types of 4-D imaging: prospective gated imaging andretrospective correlation imaging. In both types of imaging a device thatmonitors respiratory motion is attached to the patient’s chest.

Prospective gated imaging is illustrated in Figure 19.19. Duringaxial scans patients hold their breaths at either maximum inspiration ormaximum expiration. The patient then resumes breathing while thecouch is moved in. The patient then holds his breath again until the nextaxial scan is completed. The process continues until the entire scan isacquired. A disadvantage of this technique is that it requires patientcooperation and training.

In retrospective correlation (Figure 19.20) the patient breathesfreely during a helical ultra low pitch scan. The pitch is made low


Figure 19.17: Illustration of the effects of motion on CT imaging. The region of interest is a sphere thatis oscillating up and down as a result of respiratory motion. See the text for details.(Adapted from The Modern Technology of Radiation Oncology, vol. 2, J. Van Dyk (ed.),Fig. 2.5, p. 40, © 2005; previously printed in International Journal of Radiation OncologyBiology and Physics, “Can PET provide the 3D extent of tumor motion for individualizedinternal target volumes?” C. B. Caldwell, K. Mah, M. Skinner, and C. E. Danjoux, vol. 55,pp. 1381–1393, © 2003 with permission from Elsevier. )


Figure 19.18: (a) A coronal reconstruction of a free breathing spiral CT. The jagged motion artifactsillustrated in Figure 19.17 can be seen in the diaphragm. The outline of a tumor is shown.(b) An expiration-correlated image. The motion artifacts are considerably reducedalthough not completely eliminated (examine the diaphragm). The shape of the tumor isnow significantly different. (Courtesy of Rafael Vaello, TomoTherapy® Inc.)

(a) (b)

Figure 19.19: Gated prospective 4D CT. The top line shows the patient’s free breathing pattern. Themiddle line shows 4D CT gated on full expiration. The patient is asked to hold his or herbreath at full expiration while scanning is underway. This is repeated until the entire vol-ume of interest is scanned. The bottom line shows 4D CT gated on inspiration.

enough so that all portions of the anatomy are imaged through severalrespiratory cycles. The couch should not move more than one detectorlength in the time it takes to complete one breathing cycle. For a tuberotation time of about 0.5 s and a breathing rate of 12 breaths/min, thepitch should be about 0.1. The respiratory cycle is divided into phases.The operator can choose the number of phases. A typical number is 10.The slices are then arranged in groups according to the phase of the res-piratory cycle in which they were acquired. One then has 10 groups ofCT scans of the patient’s entire chest at 10 moments in time. This canresult in over 1000 axial slices. These data can then be used to study thethree-dimensional motion of lung tumors in detail. This allows an assess-ment of the internal target volume (ITV) (see chapter 14, section 14.6).

19.5 Magnetic Resonance ImagingMagnetic resonance imaging is capable of superb soft-tissue discrimina-tion. MRI is used to diagnose diseases of the central nervous system andmusculoskeletal disorders. Breast MRI is used to evaluate lesions dis-covered with mammography. MRI is widely used as an adjunct to CT inlocalizing treatment volumes, particularly in the brain. MRI is alsocapable of direct multi-planar imaging. A CT unit acquires imagesdirectly in an axial plane. Images in any other plane, such as the coro-nal or sagittal, require additional computer processing whereas MRimages can be acquired directly in any desired plane. The 2003 NobelPrize in “Physiology or Medicine” was awarded to Paul Lauterbur andPeter Mansfield “for their discoveries concerning magnetic resonanceimaging.” This Nobel Prize was somewhat controversial because another


Figure 19.20: Retrospective 4D CT. The patient breathes freely while a very low pitch scan is acquired.Every portion of the relevant anatomy is imaged through a minimum of one respiratorycycle. The breathing cycle is divided into phases. In this figure there are a total of sixphases. Eight to ten phases are common. All axial images acquired during a particularphase are grouped together into sets. See COLOR PLATE 14.

important contributor to the development of MRI, Raymond Damadian,was excluded.

An MRI imager appears much the same as a CT imaging unit (Fig-ure 19.7), although the bore is deeper. Some patients experience claus-trophobia when in the bore. It may take as long as 10 to 15 minutes toacquire a series of MRI images. A very uniform high-intensity magneticfield is established inside the bore (see chapter 2, section 2.3.6). Thefield strengths can range from 1 to 3 T and are generally produced withsuperconducting electromagnets (see chapter 2, section 2.3.4). Thesemagnets require cooling with liquid helium. Higher field strengthsallow shorter imaging time and higher signal to noise ratio. MRI unitscannot be situated near linear accelerators because the strong magneticfields would interfere with the motion of the electrons in the linac.Patients with any ferromagnetic implants may not be eligible for anMRI scan. This includes patients with pacemakers or aneurism clips,etc. Exposure to magnetic fields of the strength used for MRI are notknown to cause any significant side effects. MRI units are now avail-able with an “open” magnet configuration. These units do not have adonut and thus eliminate claustrophobia.

Nuclear magnetic resonance is based on a fundamentally quantummechanical effect. A classical physics description of this is simply notpossible. We will do our best to explain by drawing classical analogiesand “waving our hands.” Do not be distressed if you feel that you do nothave a detailed or fundamental understanding of this topic. Our taskhere is to simply provide some flavor of the basic science of MRI. Mag-netic resonance imaging is complex and requires years of study tounderstand fully.

Elementary particles possess an intrinsic angular momentum or“spin.” The comic book depiction of this is a small spinning top (likemost comic book depictions, this is not reality). A small magnetic fieldis associated with this spin. The particle acts like a tiny bar magnet (seeFigure 19.21) or a “dipole.” In an atomic nucleus protons tend to pair upwith spins in opposite directions. The same is true for neutrons. Whennucleons pair up, their magnetic fields cancel. A nucleus with an oddnumber of neutrons, protons, or both, however, will have a residual mag-netic field. Hydrogen, with a single proton, is one such nucleus. Hydro-gen is abundant in tissue and is therefore used for most MR imaging.

In the absence of an externally applied magnetic field, the magneticfields of the individual nuclei will point in random directions and thus,over the bulk of the material, they will cancel out. If an external mag-netic field is applied however, the magnetic nuclei will tend to line upwith this field, like iron filings on a piece of paper subjected to a mag-netic field. The aligned nuclei will contribute to the external field, rein-forcing it. The magnetic field associated with the aligned nuclei iscalled the “magnetization” and the symbol for this quantity is

rM .


When the nuclei, which act like little bar magnets, are subjected toan external magnetic field, they behave like a spinning top or a gyro-scope in a gravitational field. A top that is spinning will “precess” underthe action of gravity (see Figure 19.22). The rotation axis of the topslowly rotates around a vertical axis. In an analogous fashion, nucleiprecess in an externally applied magnetic field. The frequency of pre-cession is called the Larmor frequency, ν, and it is directly proportionalto the strength of the external magnetic field:

(19.4)

where γ is a quantity that depends on the particular atomic nucleus and iscalled the gyromagnetic ratio. The value of γ /2π for protons is 43 MHz/T.For a magnetic field strength of B0 � 1.5 T, the precession frequency is64 MHz. This is in the radio region of the electromagnetic spectrum justbelow FM radio in frequency (see chapter 2, section 2.4).

After the external magnetic field is applied to the patient, there arethree stages in the process of MR imaging: excitation, relaxation, anddetection. Excitation involves tipping or rotating the magnetic moment awayfrom the axis defined by using the addition of a briefly applied weak

rB0

νγ

π=

B0

2,


Figure 19.21: Elementary particles such as neutrons and protons possess a property called “spin.” A smallmagnetic field is associated with this. Elementary particles act like small bar magnets.

magnetic field in the form of a radio frequency (RF) pulse. The anglethrough which is tipped can range from 0° through 180°, dependingon the duration of the pulse. If is tipped 90°, this is called a 90° pulse.After the RF pulse, “wants” to return to its undisturbed directionalong This is relaxation.

After excitation, the amplitude of the component of in the x-yplane will decrease at a rate 1/T2 and the z-component will increase at arate of 1/T1. The values T1 and T2 depend on the external field strengthB0 and on the characteristics of different types of tissue. As the nucleireturn to their equilibrium state, they emit an RF signal which can bedetected by an RF coil. This is detection. The closer the receiving coil tothe patient, the better. A number of different types of RF coils are avail-able: head coils, body coils, and coils for other body parts.

The precession frequency depends on the applied magnetic field[see equation (19.4)]. If small gradients are deliberately introduced intothis field, then the precession frequency will vary with position in thepatient. In this way spatial information can be encoded in the data andthis information can be used to reconstruct an image.

Typical images are one of three types: proton density or spin den-sity, T1 weighted, or T2 weighted (see Figure 19.23). These are pro-duced using different combinations of echo time (TE) and repetitiontime (TR). T2 weighted images have TE of 60 to 100 ms and TR ofabout 3000 ms. T1 weighted images have TE about 10 ms and a valueof TR comparable to T1 for the tissue of interest (about 500 ms at

rM

rM


rMr

MrB0.

Figure 19.22: A spinning top precesses in a gravitational field; that is, the spin axis itself rotates arounda vertical axis. In a similar way, the magnetic moment of a proton precesses around thedirection of an externally applied magnetic field. The direction of the magnetic field istaken to be along the z-axis.

1.5 tesla).4 Fluid attenuated inversion recovery (FLAIR) is a pulsesequence that creates images that have T2 weighted contrast for braintissue but in which signals for CSF are suppressed.

FLASH stands for fast low angle shot, and about 70% of MRI isdone this way. A contrast agent that is commonly used contains theparamagnetic element gadolinium.

MR images by themselves are generally not adequate for treatmentplanning purposes. They are more susceptible to spatial distortions thanCT. It is important to have reliable geometric information about thepatient. The determination of the location of a voxel in MRI is governedby the magnetic field gradients. Any irregularities in the magnetic fieldcan therefore cause spatial distortion. In addition, MR imaging takeslonger than CT and therefore there is an increased likelihood of distor-tion due to patient motion. Furthermore, MRI does not provide informa-tion about electron density, which is necessary for inhomogeneitycorrections in dose calculations. The physical dimensions of the scannerand its accessories limit the use of immobilization devices. Dense bonecontains very little hydrogen and therefore the bone signal is weak. Forthis reason useful DRRs cannot be generated for comparison with por-tal images. Instead of being used by themselves, MRI images are oftenused in conjunction with CT data for treatment planning. This requiresimage fusion, which is discussed in the next section.


4 “MRI in Radiation Treatment Planning” by Y. Cao and L. Chen, pp. 401–424 in Integrating NewTechnologies into the Clinic: Monte Carlo and Image-Guided Radiation Therapy, AAPM 2006 Sum-mer School Proceedings, AAPM Medical Physics Monograph No. 32, B. H. Curran, J. M. Balter,and I. J. Chetty, Program Directors, 2006.

Figure 19.23: Three axial MRI images of a GBM tumor. (a) is a T1 weighted image. This image displaysthe tumor and edema as dark. (b) is T2 weighted. This image displays the tumor andedema as light. T2 images do not show fat and they highlight CSF and gray matter. Theimage in (c) was made with a gadolinium contrast agent. (Courtesy of Brigham andWomen’s Hospital, Boston, MA)

(a) (b) (c)

19.6 Image Fusion/RegistrationFor the purpose of treatment planning it is very useful to be able tocombine or correlate images from different modalities, in particular CTand MRI. Tumors frequently appear very different on MR images thanon CT (if they show up at all). Image fusion (or registration, as it issometimes called) is the process of placing two sets of images on thesame coordinate system so that they can be superimposed like an over-lay or viewed simultaneously. This correlation combines the advantagesof CT with another modality such as MRI or PET. Most treatment plan-ning systems offer the option of image fusion. Sometimes it is desiredto register two sets of CT images obtained on different dates. Theprocess of image-guided radiation therapy (IGRT; see section 19.10)depends on image registration.

We first consider the problem of registration for images of an objectthat is a rigid body. A rigid body is one that cannot change shape or bedeformed. The two objects in the different image sets can be broughtinto coincidence by coordinate translations (shifts) and rotations. It isbest if both sets of images are obtained at about the same time, ideallythe same day. The patient should be in the same position for each imag-ing modality. Ideally any immobilization devices should be used forboth sets of scans. We will discuss three methods for registration of arigid body: point-to-point matching, surface to surface matching andvoxel-to-voxel matching.5

In point-to-point matching, a set of corresponding reference pointsor fiducial markers is necessary in both sets of images. These can beexternally placed markers positioned in key locations on the patient’sskin. Adhesive markers are available commercially, which show upclearly in both CT and MRI images. A bare minimum of three points ineach image, not all lying in the same plane, is required and more arepreferred. Once the fiducial points are specified, the image fusion soft-ware shifts (translates) and rotates the images so that they correspond toone another. In the absence of externally placed markers, which arepreferable, internal anatomical reference points may be used. It may notbe easy to find anatomical points of reference that can be clearly seen inboth image sets.

Anatomical surfaces may be easier to delineate in both image setsthan discrete points. Surface matching involves matching anatomicalsurfaces in the two images. Voxel-to-voxel matching uses all of theinformation in the images. In this technique there is an attempt to cor-relate all of the voxels to one another. One shortcoming of this tech-nique is that parts of the image may be unreliable. An example is themandible, which may be in different positions with respect to the skull


5 Radiation Oncology: A Physicist’s Eye View by M. Goitein, 2008, p. 48.

in the two image sets. A method of image registration that has achievedsome success involves the maximization of “mutual information.”6

Although the pixel intensities of tissues may differ in different modali-ties, there is a relationship between them. For example, bone is bright inCT images and dark in MRI images. Mutual information registrationrelies on the predictable relationship between corresponding tissue typesin the two image sets.

If there are significant differences in the shape of the patient betweenthe two image sets, then deformable image registration is desirable. Dif-ferences in shape may result from imaging on different days, in differentpositions, or with and without immobilization devices. Respiratorymotion may cause deformation also. Deformable image registration isnot yet commonly available in commercial treatment planning software.

For treatment planning, the primary set of images is the CT set.Dose calculations are done from this set. Once the software has per-formed the fusion, it is up to the user to examine the images to assessthe quality of the result (see Figure 19.24). Do not take the quality ofthe fusion for granted. The correlation of the two image sets must becarefully examined. The radiation oncologist can draw tumor outlines(GTV, CTV, etc.) on the fused MR (or PET) images, which will thenautomatically be transferred to the CT images used for dose calcula-tions. The reliability of this process depends critically on the quality ofthe registration.


6 Chen et al., in Chapter 2, Imaging in Radiotherapy in Treatment Planning in Radiation Oncology,2nd edition (F. Khan, ed.).

Figure 19.24: An example of image fusion between CT and MRI images. The image in (a) is the CTimage. The image in (b) is the reconstructed (fused) MRI image that corresponds to this.The quality of the fusion (which is marginal) is assessed from the “checkerboard” imagein (c). Alternating squares are either CT or MRI.

(a) (b) (c)

19.7 Ultrasound ImagingThe use of ultrasound for diagnostic imaging is widespread in medi-cine. Ultrasound is one of the three means of imaging soft tissue. Ultra-sound equipment is relatively inexpensive and there is no ionizingradiation exposure. An ultrasound system is shown in Figure 19.25.Ultrasound is frequently used as an adjunct to mammography for breastcancer detection. In radiation therapy ultrasound is used for treatmentplanning, particularly for prostate brachytherapy implants, and fortreatment position verification, primarily for external beam prostatetherapy (see section 19.10).

Sound waves are longitudinal waves—a small parcel of matter in themedium oscillates back and forth in the direction in which the wavemoves (see Figure 19.26). This contrasts with transverse waves in whichthe motion of the medium is perpendicular to the direction of wavetravel (as in Figure 2.12). Examples of transverse waves are waves on astring or (approximately) waves on the surface of water.


Figure 19.25: Ultrasound imaging cart. (Courtesy of Siemens Medical Solutions USA Inc., Concord, CA)

Sound can be thought of as a compressional wave. This is illustratedin Figure 19.26. This figure shows a snapshot at an instant in time of acompressional wave.

The speed of sound in a given medium depends on the elastic prop-erties of that medium. The speed of sound in soft tissue is approxi-mately 1540 m/s. Ultrasound imaging is dependent on differences in thesound speed of various tissues. When an ultrasound wave is incidentupon an interface where the sound velocity changes, part of the wavewill be reflected. It is these reflections that form the basis for conven-tional ultrasound imaging.

The frequencies of audible sound waves extend from about 20 Hzup through perhaps 20 kHz (if you are a child with excellent hearing).Ultrasound frequencies are approximately 5 MHz, well beyond therange of human hearing (hence the name ultrasound). As an example,we will calculate the wavelength of a 3.5 MHz sound wave in soft tis-sue. We use the equation ν λ � cs [essentially equation (2.19)] where csis the sound speed: λ � cs /ν � (1540 m s–1)/(3.5�106 s–1) � 4.4�10–4 mor 0.44 mm. To achieve high spatial resolution, small wavelength isdesirable. If the wavelength is comparable to, or larger than, the objectto be imaged, then the wave will simply “bend” (diffract) around theobject and no clear (specular) reflection will occur. It is apparent fromthe previous calculation that high frequencies are necessary to achievesmall wavelength, and this is why ordinary audible sound would beinadequate for high-resolution imaging.


Figure 19.26: A longitudinal sound wave. The top portion of the figure shows an undisturbed medium(no sound wave). The bottom portion is a snapshot at a particular instant in time show-ing regions of compression and decompression. A small element in the medium movesback and forth horizontally as the wave passes by from left to right.

Ultrasound waves are produced and detected by a device called atransducer. A transducer is any device that converts one form of energyto another. The ultrasound transducer converts electrical energy tomechanical energy. An electrical signal fed into the transducer convertselectrical energy to mechanical vibrational energy. The transducer iscoupled to the patient surface (sometimes a coupling gel is used to getgood mechanical contact) and sound is transmitted into the patient’sbody. A transducer also detects and converts the reflected sound wavesinto electrical energy—similar in function to a microphone. The reflectedwave provides the basis for image formation. The longer it takes a wavereflected from an interface to return to the transducer, the further theinterface is from the transducer.

19.8 Functional/Metabolic ImagingFunctional imaging shows the location and strength of physiologicalactivity at the cellular and molecular levels.

The promise of functional imaging:

(1) Improve disease detection: functional imaging is capable ofdetecting microscopic disease.

(2) Cancer staging: functional imaging may reveal areas of diseasenot visible with anatomical imaging. For example, it may morereadily reveal the existence of metastatic disease.

(3) Treatment planning: functional imaging may be of assistance inplanning radiation therapy by providing more accurate localiza-tion of disease; radioresistance of tumor, tumor phenotype; iden-tify areas of hypoxia that may require a higher dose. In thefuture it may become possible to identify a biological targetrather than simply an anatomical target.

(4) Response to therapy: may allow a more rapid indication of cellu-lar response to therapy.

(5) Earlier detection of recurrence.

Positron emission tomography (PET) provides metabolic informa-tion such as glucose metabolism rates. Cancer cells generally metabolizeglucose at higher rates than normal cells. The patient is administered apharmaceutical tagged with a positron emitter either by injection orinhalation. PET scans frequently employ F-18 (fluorodeoxyglucose,18F-FDG). This is a marker for glucose metabolism. The distribution ofactivity throughout the patient is imaged. FDG uptake is enhanced inmost malignant tissues and in some benign structures as well. FDGuptake can be used to measure tumor response to treatment as well asfor initial staging. New PET radiopharmaceuticals that are more specificmarkers of tumor activity are under development.


F-18 undergoes positron decay with a half-life of 110 minutes. Thepositron emitters used in PET imaging have a short lifetime and there-fore the supply for these isotopes must be physically close at hand.Positron emitters are produced in cyclotrons. Therefore PET facilitiesmust either have a cyclotron on site or a cyclotron must be located rel-atively nearby.

There is a waiting period of about an hour between injection of FDGand the scan to allow time for uptake. PET scan data acquisition takeson the order of 20 minutes. This is clearly a problem when significantrespiratory motion is present. 4D PET scanning is on the horizon and isexpected to be available soon.

The positrons travel only a short distance before annihilating andforming two 0.5 MeV photons that travel in almost completely opposite(180°) directions. These photons are detected by scintillation detectorsmade of bismuth germanate (BGO) or (LSO:ce).7 The visible photonsthat emerge from the scintillator are detected by photomultiplier tubes.


7 Sasa Mutic in “Use of Imaging Systems for Patient Modeling PET and SPECT” by S. Mutic,pp. 375–400, in Integrating New Technologies into the Clinic: Monte Carlo and Image-Guided Radi-ation Therapy, AAPM 2006 Summer School Proceedings, AAPM Medical Physics MonographNo. 32, B. H. Curran, J. M. Balter, and I. J. Chetty, Program Directors, 2006.

Figure 19.27: The detectors in a PET scanner form an axial ring around the patient. Event counting isbased on annihilation coincidence. Events must occur nearly simultaneously in oppositedetectors or they are rejected. Coincidence detection confirms that the annihilation musthave occurred somewhere along the line joining the detectors. (Reprinted by permissionfrom MacMillan Publishers Ltd: Nature Reviews Cancer, vol 4, pp. 457–469, “The poten-tial of positron-emission tomography to study anticancer-drug resistance,” C. M. L. West,T. Jones, and P. Price, © 2004.)

PET uses annihilation coincidence detection to reconstruct axialimages showing the activity distribution or uptake. There is a series ofdetectors in a ring around the gantry bore (see Figure 19.27). Eachdetector in the ring is paired with detectors on the opposing side of thering. If a signal is detected in one of the detectors, a gating circuit “lis-tens” for a signal in the paired detectors on the opposite side for a shortinterval of time called the coincidence window. If a signal is detectedduring this interval, it is assumed that the signal must represent a trueannihilation photon corresponding to the detection on the opposite side.It is then known that the annihilation must have occurred somewherealong the line joining the two detectors. If no second signal is detectedduring the coincidence window, the original signal is discarded. Thecoincidence window is usually about 5 to 10 ns in duration, which cor-responds roughly to a time t � D/c, where D is the maximum thicknessof the patient and c is the speed of light.

Currently, 90% of PET scans are for oncology purposes. CombinedPET/CT scanners now completely dominate the market. In a PET/CT unitthe two gantries are combined in the same housing (see Figure 19.28).PET/CT machines have the advantage that fusion is more accuratebecause the patient is scanned on the same couch and almost at thesame time as the CT scan. Therefore the patient is positioned identicallyin the two scans. Fusion of separate PET images and CT is more diffi-cult because of the low spatial resolution of PET images (on the order


Figure 19.28: A PET/CT unit. This is a long bore design in which the housing covers both the PET and CTunit. (Reprinted from The Modern Technology of Radiation Oncology, vol. 2, J. Van Dyk(ed.), Fig. 2.14, p. 63, © 2005; previously printed in Radiologic Clinics of North America,vol. 42, issue 6, A. M. Alessio, P. E. Kinahan, P. M. Cheng, H. Vesselle, and J. S. Karp,“PET/CT scanner instrumentation, challenges, and solutions,” pp. 1017–1032, © 2004 withpermission from Elsevier.)

of 5 mm). The CT data allow for attenuation corrections of the PETimage, resulting in sharper images and significantly shorter (by up to40%) PET scan time.7

The uptake of FDG can be quantified by the use of the standarduptake value (SUV), which is defined as:

(19.5)

where the activity per unit volume is measured in units of MBq/ml, thedecay factor is the fraction of decay between administration and thetime of the scan, and the injected activity/body mass is in units ofMBq/g. The SUV will vary throughout a tissue. The maximum SUV isa more useful parameter than average SUV.8 SUV may not be useful intissue that normally has a high SUV such as the brain (high glucosemetabolism rate) and the kidneys (the kidneys clear FDG from thebody). It is common to use an SUV threshold of 2.5 as an indicator ofthe presence of malignant tissue although SUV values have not beenshown to be useful for defining GTV boundaries.9

19.9 Portal ImagingHow do we verify correct treatment delivery?

(1) Positional accuracy: Are we hitting the target?Portal imaging.

(2) Dosimetric accuracy: Are we delivering the right amount of doseto the target?In vivo dosimetry: TLDs, diodes, MOSFETs, etc., discussed inchapter 8 (see also chapter 18, section 18.3.4). In the futurethese two may be “married” with portal imagers that can simul-taneously image and verify dose.

Portal images can be acquired with either film (rapidly disappear-ing) or electronic portal imaging devices (EPIDs). Portal images areused to verify both the shape of the aperture and the position of the cen-tral axis with respect to the patient’s anatomy. It is common to super-impose an open field on the portal aperture field so that surroundinganatomy can be viewed for reference. This is sometimes referred to as a“double exposure.”

SUVActivity per unit volume decay factor

Inject=

/

eed activity body mass/,


8 The SUV must be used with caution. Caldwell and Mah have pointed out that some researchersrefer to SUV as standing for “silly, useless, value.”

9 C. B. Caldwell and K. Mah in chapter 2, Imaging for Radiation Therapy Planning, The ModernTechnology of Radiation Oncology, Volume 2, J. Van Dyk (ed.), page 67.

19.9.1 Port Films

(1) Localization film: Exposure is short compared to the daily treat-ment time, need sensitive film.

(2) Verification film: Exposure is for the duration of the treatmentdelivery with that field, use slow film such as Kodak XV film.

These films are compared with films from the simulator or DRRs pro-duced by the treatment planning system. The purpose is to verify targeting.

Why is portal image quality so poor compared to diagnostic images?

(1) Poor contrast: Predominant interaction is Compton, weakdependence on Z, very little differential absorption is seen com-pared to diagnostic films.

(2) Scattered photons and secondary electrons: Scattered photons arenot easily removed, cannot use a grid.

(3) Large penumbra: Geometric � phantom scatter.

The quality of port images degrades with increasing beam energy andpatient thickness (>20 cm). Portal images should be made using thelowest energy photon beam available.

For portal films, the film is placed in a special cassette. Comptonrecoil electrons form the image on the film, not the photons directly. Thesecondary electrons generated in the patient, treatment couch, etc., tend tosmear out images because electrons are very easily deflected. We want tofilter out these electrons. We would also like to have some build-up infront of the film. For these two reasons metal screens are used inside por-tal film cassettes. The screen is placed in close contact with the film. Thescreen is made of a high-density material such as lead or copper. It is com-mon to use a copper screen about 1 mm thick. Port films are not made inreal-time—they have to be developed. They are impractical to do beforeevery treatment. This leads to a motivation to have real-time imaging.

19.9.2 Electronic Portal Imaging Devices10

There are three major types of electronic portal imaging devices (EPIDs):

(1) Screen camera systems.(2) Matrix ion chamber.(3) Flat-panel arrays.

This field is evolving rapidly. Linac manufacturers have now moved toflat-panel arrays.


10 Much of the information in this section is taken from The Modern Technology of Radiation Oncology,J. Van Dyk (ed.), 1999.

Screen camera systems use a video camera and a mirror oriented ata 45° angle. A phosphor-coated metal plate produces visible light pho-tons, which are imaged by the camera. Camera images are digitized at30 frames/s, then averaged to produce a final image. They have goodresolution, but they are bulky and tend to get in the way.

Matrix ion chamber EPIDs consist of an array of ionization cham-bers. One design uses a 256�256 array of ion chambers with an elec-trode separation of 0.8 mm and is filled with a volatile liquid. When theliquid is irradiated, ion pairs are formed which are collected when a biasis applied between the electrodes.

Flat-panel arrays have replaced camera-based and matrix ion cham-ber EPIDs. The image quality is superior to the older technology. Theflat-panel arrays overcome the bulkiness of camera systems and the rela-tively long irradiation times for matrix ion chamber EPIDs. Flat-panelEPIDs are solid-state devices in which amorphous silicon (a-Si) isdeposited on a thin substrate, usually 1 mm of glass. Amorphous siliconis highly resistant to radiation damage and can therefore be placed in thedirect beam. Each pixel is a photodiode, which detects light generated bya screen/phosphor combination. The screen/phosphor combination con-sists of a metal plate and a phosphor screen. The metal plate removes sec-ondary electrons generated in the patient as well as low-energy scatteredphotons. A commercial model is the Varian aS500 Portal Vision with anarray size of 40�30 cm2 and 512�384 pixels (see Figure 19.29). Thismodel has a 1 mm copper plate and a gadolinium oxysulfide (Gd2O2S)screen. Each pixel value is represented by a 16-bit word.


Figure 19.29: A portal imager on a robotic arm. The imager folds away at the base of the gantry whennot in use. The arm can move the imager vertically and horizontally. (Courtesy of VarianMedical Systems, Inc. Copyright © 2010. All rights reserved.)

What are the differences between the use of EPIDs and film? Oneobvious difference is an immediate result without having to wait forprocessing. EPIDs are sensitive to the dose rate whereas film is sensi-tive to the total cumulative dose. For the EPID, one sets a specific num-ber of MU regardless of the patient thickness. For film one must takeinto account the patient thickness. The digital format of EPID imagesallows image enhancement, window and leveling, and digital storageand dissemination. Both film and EPID images are available in hardcopy. With film, what you see is what you are stuck with.

The ease of use of EPIDs makes more frequent imaging easily fea-sible (see Figure 19.30). It becomes feasible to image the patient dailyand to use correction algorithms that indicate shifts (and possibly rota-tions) of the patient with respect to the intended treatment position. Itthen becomes possible to move the patient into the intended positionjust prior to treatment.

19.10 Image-Guided Radiation TherapyImage-guided radiation therapy (IGRT) employs imaging of soft tissueor implanted markers to ensure target positioning prior to treatment. Thelocation of key anatomical structures or markers is compared to theexpected location (based on CT images used for treatment planning) and


Figure 19.30: An electronic portal image made with a flat-panel array. This is a lateral skull imagemade with a 6 MV beam using 2 MU for a whole-brain irradiation field. The graticule isvisible in the image. The faint outline of a diode placed on the patient’s skin is visible atthe center. Compare this image with the DRR for the same patient in Figure 19.16.

the patient is moved if necessary. The geometric accuracy of treatmentdelivery is limited by three factors: set up uncertainty, intrafraction tar-get movement, and interfraction target movement. These issues havebeen discussed in chapter 14, section 14.6. The desire for highlyconformal therapy is the motivation for IGRT. IGRT reduces the chanceof a geometrical miss and allows a reduction in the size of the PTV withall the benefits that follow: fewer treatment complications and/or doseescalation.

There are quite a variety of commercially available systems forIGRT. Conventional linear accelerators can now be purchased withoptional on-board kV imagers that are capable of cone beam CT (seeFigures 19.31 and 19.32). The imager consists of an x-ray tube and aflat-panel detector. The axis of the x-ray beam is perpendicular to theMV beam axis. These are now widely available. Another option is aconventional linac and a CT scanner that share a common couch. A thirdoption is CT images generated from the same MV beam that is used totreat the patient. This technique is used on an innovative treatmentmachine that delivers “tomotherapy.” We defer a discussion of tomother-apy units to the next chapter. Ultrasound is used in some clinics toimage the prostate prior to prostate radiotherapy. Yet another choice isimplantable markers that are available from several vendors. These


Figure 19.31: A conventional linac with on-board kV cone beam imaging. The gantry rotates aroundthe patient with the MV beam off and the kV beam on. Given a sufficient number of pro-jections, a set of axial CT images may be reconstructed.

markers can be observed in MV images. Provided that there are a suffi-cient number of these, the location and orientation of the organ in whichthey are embedded can be determined. Markers have been used widelyfor prostate treatments. A more exotic illustration of IGRT is provided bythe imaging capabilities of a robotic linac (see the discussion of radio-surgery in chapter 20).

For kV cone beam CT the gantry rotates around the patient while thekV x-ray tube is on and the MV beam is off. During gantry rotation thekV imaging panel is acquiring numerous projections. The projection datacan be reconstructed to provide a set of CT axial images. The shape ofthe kV x-ray beam is a cone and thus this modality is referred to as conebeam CT (CBCT). For IGRT purposes it is crucial that the MV beam andthe kV beam share the same isocenter. During gantry rotation the x-raytube and imager may sag or flex. It is necessary to correct for this by useof a “flexmap” which characterizes the flex with gantry angle.

CBCT images can be compared to the treatment planning CT. TheCBCT software on the linac allows the operator to determine the shiftin patient position that will best bring the two sets of images into align-ment (see Figure 19.33). In general, this requires three shifts (transla-tions), one in each of three perpendicular coordinate directions androtations about three axes. Rotational correction is available on somespecialized linacs. Linacs without this capability use the three transla-tions that give the best fit. If the movements are small, the table can bemoved automatically from the control console without having to enterthe treatment room.

Ultrasound is used in some clinics to image a patient’s prostate glandprior to delivery of radiation for prostate cancer (see Figure 19.34).


Figure 19.32: The Elekta Synergy® with on board kV imager. (Courtesy of Elekta, Norcross, GA)


Figure 19.33: Cone-beam image-guided radiation therapy. (a) A patient’s cranium as imaged with theElekta XVI (x-ray volume imaging) system shown in Figure 19.32. Contours of a braintumor (in red) have been imported from the treatment planning CT. This is the viewprior to image registration. The planning CT image is in pink and the cone beam CT is ingreen. There is a clear mismatch between the two sets. (b) This is the same as (a) exceptthat this is the image after registration. The patient is now positioned very accuratelyfor treatment. (Courtesy of Elekta, Norcross, GA) See COLOR PLATE 15.

Figure 19.34: Prostate ultrasound localization for IGRT. A therapist is holding the transducer againstthe patient’s skin. The head of the linac and the docking station can be seen at the topof the photo. (Courtesy of Best Medical, Springfield, VA, www.TeamBest.com)

(a) (b)

The tricky part is to register the images with the planning CT (seeFigure 19.35). The ultrasound transducer is at the end of an articulatedarm. This arm is able to keep track of both the position and orientationof the transducer. Prior to imaging the transducer is docked at a dock-ing station attached to the head of the linac. The position of the dockingstation is known with respect to the isocenter. Image information canbe referenced in this way to the linac isocenter.


Figure 19.35: A screen capture from the NOMOS BAT (B-mode Acquisition and Targeting) ultrasoundIGRT system. The image on the left is an axial image. A sagittal image is shown on theright. The operator has superimposed contours of the bladder, GTV, and rectum from thetreatment plan. These contours have been aligned with the corresponding structuresin the ultrasound images. The shift necessary to bring about this alignment on thecomputer is then used to calculate how the patient should be moved. This informationis shown in the box on the lower right. (Courtesy of Best Medical, Springfield, VA,www.TeamBest.com) See COLOR PLATE 16.

Chapter Summary• Imaging for Treatment Planning(i) Plane film(ii) Fluoroscopy

(iii) CT(iv) MRI(v) Ultrasound

• Digital images are composed of picture elements called pixels; radio-logical images are usually 512�512 pixels.

• Gray Scale: The number of levels of gray assigned to a pixel; thisdetermines the contrast resolution of the image; an 8-bit gray scalehas 28 � 256 shades of gray.

• CT: Provides three-dimensional reconstruction of patient anatomyand electron density data for inhomogeneity corrections.

—Image reconstruction: Need a sufficient number of projections tocalculate µ for each voxel.

—Image size usually 512�512 pixels; requires about 0.5 MB/slice forstorage

— where µt is linear attenuation coefficient for

tissue in a particular voxel and µw is the linear attenuation coeffi-cient for water.

—CT# sometimes called Hounsfield units (HU). CT#’s range between–1000 and �3000. For air CT# � –1000, for water CT# � 0, fordense bone 1300–1600.

—Window and level: Level is center value of CT# displayed and win-dow is range.

—Modern scanners are spiral multislice units.

—Pitch � (table travel per tube rotation)/(total length of tissue irra-diated by the cone beam).

—Pitch < 1: improvement in image quality but increase in dose.

—Diagnostic CT scanners: Bore diameter 70 cm; concave couch top.

CT # ,=−

1000µ µ

µt w

w


Conventional

3-D & soft tissue discrimination

—CT simulators: Bore diameter 80 to 90 cm; flat couch top; move-able external lasers

—Relative electron density for patient treatment planning derivedfrom calibration curve plot of relative electron density vs. CT#.

• DRR: Digitally reconstructed radiograph; simulated radiographmathematically calculated from CT data, usually beam’s-eye view foreach treatment port.

• 4D CT: Adds time dimension to the three spatial dimensions to assessor manage motion(1) Prospective gated imaging: Breath hold at either inspiration or

expiration while scanning(2) Retrospective/correlation imaging: Patient breathes freely and CT

slices are binned according to phase of respiratory cycle duringwhich they were acquired.

• MRI: Magnetic resonance imaging uses non-ionizing RF radiation,based on magnetic properties of protons in tissue

—Magnetic field strengths of 1 to 3 T

—Contraindicated for patients with ferromagnetic implants: pace-makers, aneurism clips, etc.

—Proton precesses with Larmor frequency (in the radio

region of the spectrum), where γ is a constant called the gyromag-netic ratio.

—Magnetic field gradients used so that Larmor frequency varies withposition throughout patient

—Three stages for imaging:(1) Excitation: tip direction of magnetic field of proton(2) Relaxation: magnetic field of proton returns to equilibrium

with associated time scales T1 and T2(3) Detection: detect “echo” from relaxation images are weighted

by spin density, T1 or T2

—MRI images are usually not used directly for treatment planningbecause:(1) They are subject to geometric distortion.(2) They do not provide electron density information for inhomo-

geneity corrections.

νγ

π=

B0

2


(3) Bone signal is weak, hard to produce useful DRRs for treat-ment verification.

• Ultrasound Imaging: Uses high-frequency sound, sound reflects offboundaries between tissues having different sound speeds.

—Speed of sound in soft tissue cs � 1540 m/s; ultrasound frequencyis approximately 5 MHz.

—Transducer: Converts mechanical energy to electrical energy andvice versa; used to produce and detect ultrasound.

• PET: Positron emission tomography; images the distribution of positron-emitting radiopharmaceutical throughout the body; metabolic imaging.

—Coincidence detection: Events are counted only if seen nearlysimultaneously on opposite sides of ring.

—Common radioisotope is 18F (T1/2 � 110 min), incorporated inglucose analog FDG; malignant cells exhibit enhanced glucoseuptake.

—Standard uptake volume (SUV):

—High SUV is a sign of possible malignancy.

• Imaging for Treatment Verification (Portal Imaging)(i) Film(ii) Electronic portal imaging devices (EPIDs)

—A screen is used to filter out electron contamination and to providesome build-up.

—Poor quality is due to:(1) Poor contrast: Predominant interaction is Compton, weak

dependence on Z; very little differential absorption is seencompared to diagnostic films.

(2) Scattered photons and secondary electrons: Scattered photonsare not easily removed, cannot use a grid.

(3) Large penumbra: Geometric � phantom scatter.

—The quality of port images degrades with increasing beam energyand patient thickness (>20 cm).

SUVActivity per unit volume decay factor

Inject=

/

eed activity body mass/


• IGRT: Image-guided radiation therapy; large variety of methods areused to assure correct geometric targeting:(1) Cone beam CT (CBCT): X-ray tube and flat-panel detector

attached to linac.(2) MV CT: Use megavoltage beam to produce CT image: tomother-

apy unit.(3) Ultrasound image registration for prostate treatment.(4) Implanted markers.

Problems1. An axial CT image has a field of view of 250 mm in width. The

image is 512�512 pixels. What is the pixel size? What is thesmallest object that you are likely to be able to perceive?

2. Estimate the computer storage requirements for 100 CT axial sliceimages used for treatment planning. Assume that the images are512�512, 16-bit gray scale. Give the answer in MB.

3. Estimate the time necessary to transfer these 100 CT slices over anetwork with a speed of 10 Mbps (megabits per second).

4. At a particular kVp, µw � 0.267 cm–1, and for a particular sampleof bone µbone � 0.511 cm–1. Calculate the CT# of this bone.

5. List the following tissues in order of increasing Hounsfield number:bone, muscle, fat, lung.

6. The window and level of a CT image are chosen as �300 and �100,respectively. What CT#’s are displayed as black? What CT#’s aredisplayed as white?

7. A CT scanner with a 24-mm wide detector is operated at a pitch of0.06 for a 4-D respiratory scan. How far does the table move dur-ing one tube rotation?

8. How can the quality of DRRs be improved?

9. Briefly describe the three stages in the process of MR imaging.

10. What are the contraindications for MR imaging?

11. What are the relative advantages and disadvantages of CT andMRI for treatment planning?


12. What contrast agent is frequently used in MR imaging?

13. How is the quality of portal images affected by beam energy?

14. Why do MV portal images show lower bone/soft tissue contrastthan kV images?

BibliographyAlessio, A. M., P. E. Kinahan, P. M. Cheng, H. Vesselle, and J. S. Karp. (2004). “PET/CT

scanner instrumentation, challenges, and solutions.” Radiol Clin North Am 42(6):1017–1032.

American Association of Physicists in Medicine Report No. 24. Radiotherapy PortalImaging Quality. Report of AAPM Task Group No. 28. New York: American Insti-tute of Physics, 1988.

Bushong, S. C. Radiologic Science for Technologists: Physics, Biology, and Protection, 9th

edition. St. Louis: Mosby, 2008.Caldwell, C. B., and K. Mah. “Imaging for Radiation Therapy Planning.” Chapter 2 in

The Modern Technology of Radiation Oncology, Vol 2. J. Van Dyk (ed). Madison,WI: Medical Physics Publishing, pp. 31–89, 2005.

Caldwell, C. B., K. Mah, M. Skinner, and C. E. Danjoux. (2003). “Can PET provide the3D extent of tumor motion for individualized internal target volumes? A phantomstudy of the limitations of CT and the promise of PET.” Int J Radiat Oncol BiolPhys 55:1381–1393.

Chen, G. T. Y., C. A. Pellizzari, and E. R. M. Rietzel. “Imaging in Radotherapy.”Chapter 2 in Treatment Planning in Radiation Oncology, 2nd edition. F. Khan (ed.),Philadelphia: Lippincott Williams and Wilkins, pp. 11–32, 2007.

Cody, D., and O. Mawlawi (Program Directors). The Physics and Applications of PET/CTImaging. Proceedings of the AAPM 2008 Summer School. AAPM Medical PhysicsMonograph No. 33. Madison, WI: Medical Physics Publishing, 2008.

Coia, L., T. Schultheiss, and G, Hanks (eds.). A Practical Guide to CT Simulation.Madi-son, WI: Advanced Medical Publishing, 1995.

Curran, B.H., J. M. Balter, I. J. Chetty (Program Directors). Integrating New Technologiesinto the Clinic: Monte Carlo and Image-Guided Radiation Therapy. Proceedings of theAAPM 2006 Summer School. AAPM Medical Physics Monograph No. 32.Madison, WI: Medical Physics Publishing, 2006.

Goitein, M. Radiation Oncology: A Physicist’s-Eye View. New York: Springer, 2008.Hazle, J. D., and A. L. Boyer (eds.). Imaging in Radiation Therapy. Proceedings of the

AAPM 1998 Summer School. AAPM Medical Physics Monograph #24. Madison,WI: Medical Physics Publishing, 1998.

Herman, M. G., J. M. Balter, D. A. Jaffray, K. P. McGee, P. Munro, S. Shalev, M. VanHerk, and J. W. Wong. (2001). “Clinical use of electronic portal imaging: report ofAAPM Radiation Therapy Committee Task Group 58.” Med Phys 28(5):712–738.Also available as AAPM Report No. 75.

Kevles, B. Naked to the Bone: Medical Imaging in the Twentieth Century. New York:Perseus Publishing, 1997.

McCullough, C. H., and F. E. Zink. (1999). “Performance evaluation of a multi-slice CTsystem.” Med Phys 26:2223–2230.

Mutic, S. “Use of Imaging Systems for Patient Modeling PET and SPECT” in Integrat-ing New Technologies into the Clinic: Monte Carlo and Image-Guided RadiationTherapy. AAPM 2006 Summer School Proceedings, AAPM Medical PhysicsMonograph No. 32. B. H. Curran, J. M. Balter, and I. J. Chetty, Program Directors,pp. 375–400, 2006.


Podoloff, D. A., R. H. Advani, C. Allred, A. B. Benson 3rd, E. Brown, H. J. Burstein,R. W. Carlson et al. (2007). “NCCN task force report: Positron emission tomogra-phy (PET)/computed tomography (CT) scanning in cancer.” J Compr Canc Netw5(Suppl. 1):S1–S23.

Van Dyk, J. (ed.). The Modern Technology of Radiation Oncology. Chapters 4, 5, 6, 7, and13. Madison, WI: Medical Physics Publishing, 1999.

Van Dyk, J., and K. Mah. “Simulation and Imaging for Radiation Therapy Planning.”Chapter 8 in Radiotherapy Physics in Practice, 2nd edition. J. R. Williams and D. I.Thwaites (eds.). Oxford, UK: Oxford University Press, 2000.

West, C. M. L., T. Jones, and P. Price. (2004). “The potential of positron-emissiontomography to study anticancer-drug resistance.” Nat Rev Cancer 4:457–469.


I-1

Aα (alpha) particles. See alpha (α) particlesAAPM. See American Association of Physicists

in MedicineABR. See American Board of Radiologyabsolute dosimeter, 8-8absorbed dose

defined, 7-7, 7-24ion chamber calibration, 11-6f

absorbed dose to air, 7-13–7-14absorption edges, 6-5fabsorption, photon, 5-13, 16, 26accelerating waveguide, 9-2, 9-4f, 9-6f, 9-7,

9-8f, 9-9–9-12, 9-9f, 9-10f, 9-11f, 9-12f,9-14, 9-16, 9-22–9-24, 9-23f, 9-41, 9-45

acceleratorsdielectric wall, 20-64–20-65proton laser, 20-64proton therapy, 20-44–20-51

acceptance testing, 18-3, 8-25Accredited Dosimetry Calibration Laboratory

(ADCL), 8-13, 11-4–11-5, 18-14ACMP (American College of Medical

Physics), 18-2ACR. See American College of Radiologyactinium decay series, 3-11active scanning, 20-54–20-55, 20-70activity

See also radioactivitydefined, 3-13, 3-36radioactivity, 3-13–3-14, 16-3

ADCL. See Accredited Dosimetry CalibrationLaboratory

added filtration, 5-9, 5-26adjacent fields, 14-74AEC (automatic exposure control), 4-15AFC (automatic frequency control)

plunger, 9-13fafterloader, HDR system, 16-2, 16-3, 16-6,

16-23, 16-29, 16-36–16-39, 16-37fafterloader, pulsed dose rate (PDR), 16-2air kerma strength, 16-17fALARA principle, 17-14, 17-16, 17-41alpha (α) particles

bombarding, 2-23fproperties of, 2-23, 3-2, 3-10t, 6-21radiation weighting factor, 17-5tradioactive decay of nucleus, 3-11radon, 17-7

Alpha Cradle®, 14-69, 70falpha decay, 3-19, 37Alvarez, Luis, 9-40

AM frequency, 2-18American Association of Physicists in

Medicine (AAPM)beam calibration, 11-2ion chamber calibration, 11-5quality assurance, 18-2Secondary Standards Laboratories, 8-13

American Board of Radiology (ABR), 1-1,A-1–A-11

American College of Medical Physics(ACMP), 18-2

American College of Radiology (ACR), 18-2American Registry of Radiologic Technologists

(ARRT), A-13–A-19American Standard Code for Information

Interchange (ASCII), 19-4ammeter, 2-9Anderson, Carl D., 3-9angular tolerances, linear accelerator, 18-4anisotropic source, 16-12annealing schedule, 20-17annihilation radiation, 3-9, 6-9annual effective dose, 17-41anode

GM tube, 8-23fhooded, 4-9, 4-10fstationary and rotating, 4-7fx-ray tube, 4-2f, 3

anthropomorphic phantoms, 8-3–8-4antimatter, 3-9antiparticle, 3-9aperture-based optimization, IMRT, 20-22, 20-66applicators

brachytherapy, 16-7–16-10electron, 15-5, 15-23Fletcher-Suit applicator, 16-29, 16-30f, 16-43

Aquadag™, 8-12Aquaplast® materials, 14-69arc therapy, 14-41–14-43area over perimeter rule, 10-17–10-18ARRT. See American Registry of Radiologic

Technologistsarteriovenous malformations (AVMs), 20-28ASCII (American Standard Code for Information

Interchange), 19-4asymmetric jaws

defined, 13-31dose rate calculations for shaped fields,

13-26–13-28overview, 13-2–13-3

Atomic Energy Act (1959), 17-3atomic mass unit, defined, 3-35

Index

Note: Page ranges are shown using longer dashes; an f denotes a figure; a t denotes a table.

I-2 INDEX

atomic nucleiactivity, 3-13–3-14antimatter, 3-9basic properties, 3-2–3-3decay diagrams, 3-24–3-26four fundamental forces of nature, 3-3–3-5half-life, 3-14–17mathematics of radioactive decay, 3-11–3-13mean-life, 3-18modes of decay, 3-19–3-24nuclear binding energy, 3-5–3-6production of radionuclides, 3-30–3-34properties of nuclei and particles, 3-9–3-10radioactive equilibrium, 3-26–3-30radioactivity, 3-10–3-11stability of nuclei, 3-6–3-8

atomic number Z, 2-24, 3-8fatomic structure, 2-22–2-28attenuation by matter, 5-16–5-18Auger electron emission, 3-20automatic exposure control (AEC), 4-15automatic frequency control (AFC)

plunger, 9-13fauxiliary subsystems, linear accelerator,

9-22–9-24avalanche ionization, 8-24AVMs. See arteriovenous malformations

Bbackground radiation, 17-6–17-7, 17-41backscatter factor (BSF), 10-13–10-14, 10-21backscattering, 6-7, 7-12, 14-44, 15-14, 15-15,

15-16, 18-13badges, radiation, 17-27f, 17-28BANG gel, 8-36base e, 1-4–1-7BAT (B-mode Acquisition and Targeting), 19-46fbeam analyzers, 18-8–18-9beam calibration, 11-1. See also megavoltage

photon beamsbeam divergence, Inverse Square Law, 5-14–5-16beam energy, 5-7, 5-10f, 5-17, 5-21, 9-16, 9-18,

9-22, 9-26, 9-41, 9-42, 9-45beam flatness, 9-43beam hardening, 5-9, 14-24beam profiles, 9-33f–9-34fBEAM software, 7-21beam spoilers, 14-48, 14-73beam stopper, 9-28f, 17-34beam symmetry, 9-43beam weighting, parallel-opposed fields,

14-18–14-20beamlets (bixels), IMRT, 20-65beam’s-eye view (BEV), 13-1, 13-7f,

13-11f, 20-22becquerel, 3-13, 3-36, 3-37, 16-3bellyboard, 14-69, 14-70fbending magnets, linear accelerators, 9-22

benign tumors, 20-28beta (β) particles, 3-11beta decay, 3-38

β– decay, 3-20–3-22β+ decay (positron decay), 3-23, 3-25felectron capture, 3-23–3-24

betatrons, 3-34BEV. See beam’s-eye viewbias voltage, 8-12, 8-22biological effects of radiation

carcinogenesis, 17-9–7-11genetic effects, 17-14overview, 17-8–17-9risk to fetus/embryo, 17-11–17-14

bixels (beamlets), IMRT, 20-65block cutter, 13-5fblock tray, 13-4fblocked (irregular) fields

approximate methods for estimatingequivalent square, 13-13–13-17

defined, 13-10, 13-31, 13-32dose rate calculations, 13-10

blocked region, 13-28–13-31blocking, defined, 13-1, 15-24blocks

cast, 13-3–13-6, 13-9, 13-31defined, 13-31focused, 13-4fhand, 13-3, 13-4f, 13-31

B-mode Acquisition and Targeting(BAT), 19-46f

BNCT. See boron neutron capture therapyBohr model, 2-24Bohr, Neils, 2-24, 3-21bolus, 8-28, 14-46–14-48, 14-73boron neutron capture therapy (BNCT), 3-33brachytherapy, 3-1

accumulated dose from implants, 16-20–16-21along and away calculations, 16-34–16-35applicators, 16-7–16-10dose rate calculations from exposure rate,

16-13–16-17exposure rate constant, 16-10–16-13high dose rate (HDR) remote afterloaders,

16-36–16-40intracavitary treatment of cervical cancer,

16-29–16-34localization of sources, 16-36, 16-37foverview, 16-1–16-2radioactive sources, 16-3–16-7radioactivity, 16-2–16-3source strength, 16-10–16-13, 16-17–16-18systems of implant dosimetry, 16-21–16-28Task Group 43 Dosimetry, 16-18–16-20

Bragg peak, 6-20–6-22, 6-22f, 6-26,20-42–20-44, 20-51, 20-53–20-54,20-58, 20-61–20-64, 20-69

breast board, 14-70f, 19-18f

INDEX I-3

breast cancer, field matching, 14-62–14-65, 14-74bremsstrahlung tail, 15-4, 15-23bremsstrahlung x-rays

defined, 5-25directional dependence of, 5-12filtered, 5-6foverview, 5-4–5-5unfiltered, 5-6f

broad beam attenuation, 5-18BSF (backscatter factor), 10-13–10-14build-down phenomenon, 14-16build-up cap, 8-10, 8-14fbuild-up region, 7-10, 14-44–14-46, 14-48, 20-18

Ccalibration. See also megavoltage photon beams

defined, 11-14independent check of, 11-13

calorimeters, 8-2, 8-36–8-37, 8-43camera-based frameless imaging systems, 20-30carbon-14, 17-7carcinogenesis, 17-9–17-11, 17-42carriers, 3-14cast blocks, 13-3–13-6, 13-9, 13-31catheter, 16-8cathode rays, 5-22cathodes

GM tube, 8-23fx-ray tube, 4-2f, 4-3

cavity ionization chambers, 8-8–8-12cavity magnetron, 9-40CBCT (cone beam CT), 19-44CCTV (closed-circuit television)

HDR afterloaders, 16-40radiation safety, 17-25safety checks, 18-10

CDRH (Center for Devices and RadiologicalHealth), 17-2

cDVH (cumulative dose volume histogram),14-36

ceiling lasers, 18-4–6Center for Devices and Radiological Health

(CDRH), 17-2central axis dose distribution, 10-1–10-24

backscatter, 10-13–10-14dependence of dm on field size and SSD,

10-10–10-11equivalent squares, 10-16–10-17linear interpolation, 10-18–10-19overview, 10-1–10-4peak scatter factors (PSF), 10-13–10-14percent depth dose (PDD), 10-4–10-10tissue-air ratio (TAR), 10-11–10-12tissue-maximum ratio (TMR), 10-14–10-16tissue-phantom ratio (TPR), 10-14–10-16

centripetal acceleration, 2-3, 2-4fCerrobend® metal, 13-3cervical cancer, 16-2, 16-4, 16-9f, 16-29, 16-30

cesium-137, 3-1, 16-4CET (coefficient of equivalent thickness), 15-18CFR (Code of Federal Regulations), 17-2chain reaction, 3-31fcharacteristic x-rays, 5-2–5-4, 5-25charge

collection and measurement, 8-17–8-21Coulomb force and, 2-6–2-8

Charged Particle Equilibrium (CPE), 7-4, 7-24charged particle interactions

equilibrium, 7-4matter, 6-11–6-21

chemical dosimetry, 8-2, 8-37, 8-43circuit symbol, ammeter, 2-10circular accelerators, 9-2, 20-44, 20-69circulator, 9-10Clarkson Integration, 13-17–13-22, 13-32clinical target volume (CTV), 14-31–14-32, 14-72closed-circuit television (CCTV). See CCTV

(closed-circuit television)cobalt-60 (Co-60) teletherapy units

overdose, 18-24overview, 9-26–9-31, 9-42safety precautions for, 17-26–17-27

Code of Federal Regulations (CFR), 17-2coefficient of equivalent thickness (CET), 15-18coherent (elastic) scattering, 6-3, 6-24collecting volume, 8-7fcollimated radiation, 9-36fcollimator, medical linear accelerator, 9-3fcollimator scatter, 12-5collision avoidance system, linear

accelerators, 9-25collision kerma, 7-7collisional energy loss, 6-15commissioning, 18-25committed dose equivalent, 17-4common log, 1-8complex immobilization devices, 14-68Compton scattering, 7-5, 7-16, 7-18, 7-19, 7-21,

7-25, 14-52, 17-37, 17-45computed tomography (CT). See CT (computed

tomography)cone beam CT (CBCT), 19-44cone beam IMRT, 20-7, 20-65conservation of energy principle, 2-6conserved electrical charge, 2-7constancy checks, beam calibration, 11-2,

11-12–11-13continuous slowing down approximation

(CSDA), 6-19continuous spectrum, 5-5continuous x-rays. See bremsstrahlung x-rayscontrol console, HDR system, 16-38controlled area, defined, 17-43conventional radiation therapy, 20-3fconventional simulators, 19-7–19-10coplanar beams, 14-28

I-4 INDEX

Cormack, A.M., 19-10cosine function, 1-14cosmic rays, 3-9, 17-7couch support, linear accelerators, 9-26Coulomb force, 2-6–2-8CPE (Charged Particle Equilibrium), 7-4, 7-24craniospinal irradiation, 14-59, 14-60fcritical mass, 3-31critical temperature, 2-11Crookes, William, 5-23Cs-137 source, 3-25, 3-31, 3-32, 3-41, 16-4

decay scheme, 3-26fDose Rates (cGy/h) per mgRaEq, 16-34tproperties of, 3-30t, 16-7t, 16-13, 16-15, 16-29,

16-34, 16-34t, 16-35, 16-41, B-7ttube, 16-4f, 16-7f

CSDA (continuous slowing downapproximation), 6-19

CT (computed tomography), 19-10–19-274D, 19-24–19-27defined, 19-47–19-48digitally reconstructed radiograph (DRR),

19-23–19-24Hounsfield units (HU), 19-21–19-23image reconstruction, 19-19–19-21scanners, 19-12–19-19virtual simulation, 19-24

CTV (clinical target volume), 14-31–14-32, 14-72cumulative dose volume histogram (cDVH), 14-36current, electricity, 2-9–2-10curve of binding energy, 3-6fCyberKnife® (Accuray), 20-30, 20-31, 20-32,

20-34, 20-68cyclotrons, 3-34, 20-45–20-49

defined, 20-70superconducting, 20-64

cylindrical collimators, 20-32f

DDamadian, Raymond, 19-28daughter nucleus, 3-7, 3-10decay, radioactive, 3-10

alpha decay, 3-19beta decay, 3-20–3-24defined, 3-7diagrams, 3-24–3-26electromagnetic decay, 3-19

decay series, 3-11dees (D), 20-46–20-48, 20-70deep dose equivalent, 17-4delta rays, 6-15, 6-26densitometer

defined, 8-30manual, 8-31f

Department of Transportation (DOT), 17-2depth dose

calculations, 12-8, 12-9, 13-12, 13-32,C-2–C-5, C-15

curve, 9-33, 9-35, 10-6f, 15-2, 15-2f, 15-3f,15-4, 15-7, 15-7f, 15-34

defined, 10-5, 15-22derived unit, 2-1detection, MR imaging, 19-30detection, radiation

See also gas ionization detectors; solid-statedetectors

overview, 8-38–8-43phantoms, 8-3–8-5

deterministic effects, radiation, 17-9, 17-41deterministic method, inverse treatment

planning, 20-15deuterium, 3-2deuterons, 3-5, 3-10tdiagnostic tubes, 4-17DICOM (Digital Imaging and Communication

in Medicine) standard, 19-7dielectric wall accelerators, 20-64–20-65digital images, 19-4, 19-47Digital Imaging and Communication in Medicine

(DICOM) standard, 19-7digitally reconstructed radiograph (DRR), 13-6,

19-23–19-24, 19-48diodes, 8-2

defined, 8-42solid-state detectors, 8-33–8-35in vivo dosimetry, 18-17–18-19

Dirac, Paul, 3-9direct mechanism, 7-22directly ionizing, 6-1distal blocking, 20-61distance factor, radiation exposure, 17-14distance indicator, 18-8distance to agreement, 20-25division, of exponentials, 1-3DMLC (dynamic MLC), 20-8, 20-65door, linear accelerator, 9-25

interlock, 9-25, 17-24shielding, 6-11, 16-40

dose buildup, 7-9–7-13dose calculations, proton radiotherapy, 20-56–20-61dose compensation compensator, 14-49dose distribution

arc or rotation therapy, 14-41–14-43beam spoilers, 14-48bolus, 14-46–14-48dose-volume specification and reporting,

14-31–14-34evaluation of patient dose distributions,

14-34–14-41field matching, 14-58–14-67geometric phantom, 20-4–20-5immobilization devices, 14-67–14-71in implants, 16-27–16-28isodose charts, 14-2–14-6multiple beams, 14-28–14-31parallel-opposed fields, 14-14–14-20

patient positioning, 14-67–14-71skin contour, 14-6–14-13surface dose, 14-44–14-46tissue compensators, 14-48–14-50tissue inhomogeneities, 14-50–14-58wedges, 14-20–14-28

dose from permanent implant, 16-42dose in free space, 7-17, 7-25dose in medium, 7-14–7-17dose matrix, 14-36dose rate calculations

for asymmetric jaws, 13-32dose rate at arbitrary distance, 12-12–12-16See also electron beam dosimetryequivalence of PDD and TMR calculations,

12-16–12-17from exposure rate, 16-13–16-17isocentric calculations, 12-11–12-12percent depth dose calculations, 12-8–12-11See also field shaping, shaped fieldswith wedges, 14-27–28

dose to a medium, 7-25dose to air, 7-25dose-area histogram, 14-34, 14-35tdose-volume histogram (DVH), 14-34,

14-36–14-38, 14-39f–14-40f, 14-72, 20-11dose-volume specification and reporting,

14-31–14-34dosimetry

and beam calibration, 11-13checking linear accelerators, 18-8–8-10,

8-12–8-13instrumentation, 18-15mailed program, at RPC, 11-13stereotactic radiosurgery (SRS), 20-40tolerances, 18-4–18-5t

DOT (Department of Transportation), 17-2DRR (digitally reconstructed radiograph), 13-6,

19-23–19-24, 19-48dual photon energy linear accelerator, 9-4fDVH. See dose-volume histogramdynamic MLC (DMLC), 20-8, 20-65dynamic wedge, 14-21

EEBF (electron backscatter factor), 15-14EC (electron capture), 3-23–3-25, 3-38–3-39edge effects, 15-20effective dose, 17-41effective SSD method, 14-11–14-12efficiency, x-ray production, 5-26EGS4 (electron gamma shower), 7-21Einstein, Albert, 2-19–2-20elastic (coherent) scattering, 6-3, 6-24elastic collision, 6-12electric fields, 2-8–2-9electricity

Coulomb force and, 2-6–2-8

current, 2-9–10electric fields, 2-8–2-9potential difference, 2-10–2-12

electric/magnetic force, 3-4electromagnet, 2-15electromagnetic decay, 3-19, 3-37electromagnetic spectrum, 2-16–2-20electrometer, 2-7, 2-8f, 8-17–8-18, 8-33,

8-34f, 8-40electron applicators, 15-5, 15-23electron backscatter factor (EBF), 15-14electron beam bremsstrahlung tail, 15-4telectron beam dosimetry, 15-1–15-26

calibration, 11-1, 11-13dose rate calculations, 15-9–15-14electron applicators, 15-5field matching, 15-21–15-22field shaping, 15-6–15-8inhomogeneities, 15-18–15-20internal blocking, 15-14–15-16isodose curves, 15-16–18overview, 15-1–5

electron capture (EC), 3-23–3-25, 3-38–3-39electron contamination, 11-9, 14-44electron cutouts, 15-6, 15-10electron gamma shower (EGS4), 7-21electron gun, 9-42electron linear accelerators. See linear

acceleratorselectron volt (eV), 2-12–2-14electronic portal imaging devices (EPIDs),

19-40–19-42electrons

depth dose curve, 15-2finteractions with matter, 6-14–6-15properties of, 3-10t

electrostatic unit, 7-3electroweak theory, 3-4Elekta internal wedge, 14-21Elekta MLC, 13-9Elekta Synergy®, 19-44felementary charge, 2-7elution, 3-29energy, 2-5–2-6, 2-21–2-22energy absorption coefficient, 7-5energy conservation, 2-5–2-6, 3-21energy fluence, 7-4energy transfer coefficient, 7-5entryway, treatment room, 17-39–40, 44EPIDs (electronic portal imaging devices),

19-40–19-42equipment quality assurance, 18-2–18-15

dosimetry instrumentation, 18-15linear accelerators, 18-4–18-13NRC regulations pertaining to QA, 18-13–18-15

equivalent dose, defined, 17-41equivalent mass of radium, 16-42equivalent squares, 10-16–10-18

INDEX I-5

equivalent tissue-air ratio (ETAR) method,14-52, 14-56

equivalent uniform dose (EUD), 14-40EUD (equivalent uniform dose), 14-40eV (electron volt), 2-12–2-14excitation, MR imaging, 19-29excited state

atoms, 2-25–2-26, 2-27fnucleus, 3-20

exponent (power), 1-2exponential, defined, 1-2exponential raised to a power, 1-3exponents, 1-2–1-7

base e, 1-4–1-7division, 1-3exponential raised to a power, 1-3multiplication, 1-3product raised to a power, 1-4

exposuredefined, 7-24overview, 7-2–7-4

exposure rate, 6-13, 6-17constant, 6-10, 6-18defined, 6-11, 16-17, 16-41timer error, 9-29–9-30, 9-42x-ray attenuation, 5-12

external beam radiation therapy unitsSee also cyclotronsSee also linear acceleratorscobalt-60 (Co-60) teletherapy units, 9-26–9-31overview, 9-41–9-43photon beam characteristics, 9-31–9-40

external wedge, 14-20eye shields, 15-16, 15-16f

FFaraday, Michael, 5-22Farmer ion chamber, 8-13, 8-14f, 11-5, 11-7fFDA (Food and Drug Administration), 5-10, 17-2Fermi, Enrico, 3-22Fermilab, 20-41ferromagnetic elements, 2-14fetus/embryo

dose limits, 17-16risk, 17-11–17-13, 17-42

field matchingdefined, 14-58electron beam dosimetry, 15-21–15-22overview, 14-58–14-67, 14-74

field shapingdefined, 13-1, 15-24electron beams, 15-6–15-8photon beams, 13-1–13-10, 1-32proton therapy, 20-52–20-55, 20-70

film scanner, 8-30, 8-31ffilm, x-ray, 4-10–4-13, 4-17, 8-2, 8-29–8-33filtered bremsstrahlung, 5-6ffiltration, defined, 5-26

fission byproducts, 3-30–3-32FLAIR (fluid attenuated inversion

recovery), 19-31flange, Fletcher-Suit applicator, 16-30fflat cavity (plane-parallel ion chambers),

8-15–8-16, 11-13flat-cavity chambers, 8-11, 8-39flatness, beam, 9-19, 9-25, 9-34, 9-35f, 9-42,

9-43, 18-13, 18-25tflattening filter, 6-22, 9-16, 9-17, 9-21, 9-22,

9-34, 9-38, 9-42, 14-6, 18-13, 18-24, 20-7,20-52, 20-53

Fletcher-Suit applicator, 16-29, 16-30f,16-32, 16-43

fluence, 7-4, 7-24fluorescence, 3-20FM frequency, 2-18foam polyurethane casts, 14-69focal spot, 4-5, 4-16focused blocks, 13-4ffocused collimator, 9-38fFoley catheter, 16-33Food and Drug Administration (FDA), 5-10, 17-24D computed tomography (4D CT), 19-24–19-27,

19-48four-field box beam arrangement, 14-29fframeless targeting, 20-29free radicals, 7-22free-air ionization chamber, 8-6–8-8French catheter, 16-8frequency

definition, 2-17Larmor, 19-29ultrasound, 19-35

frequency, wave, 2-17front pointer, 18-8, 18-9ffunctional disorders, 20-28functional imaging, 19-36–19-39fundamental forces of nature, 3-3–3-5

GG factor, chemical dosimetry, 8-37GAFChromic film, 8-33gamma camera, 3-29gamma emission, 3-19–3-20Gamma Knife®, 20-29f, 20-34–20-37, 20-67gamma rays, 2-19, 3-10, 17-7Gamma Stereotactic Units, 20-68gantry

angling, 9-3f, 18-11IBA cyclotron, 20-57fisocentric, 20-55f

gas amplification factor, 8-22gas ionization detectors, 8-2, 8-38

cavity ionization chambers, 8-8–8-12charge collection and measurement, 8-17–8-21free-air ionization chamber, 8-6–8-8Geiger-Müller (GM) counter, 8-22–8-25

I-6 INDEX

plane-parallel ion chambers, 8-15–8-16properties, 8-25fproportional counters, 8-21–8-22survey meter ion chambers, 8-16–8-17thimble chambers, 8-12–8-15

gas multiplication, 8-40Geiger, Hans, 2-23Geiger-Müller (GM) counter, 8-2, 8-22–8-25,

16-39, 17-40generator, x-ray, 4-13–4-15geometric penumbra, 9-36–9-37, 9-43geometric phantom, 8-3–8-4, 20-4–20-5geometry, 1-11–1-13geometry factor, TG-43, 16-19grand unified theories (GUTs), 3-4gravitational force, 3-4gray scale, 19-5, 19-47grid, x-ray, 4-17gross tumor volume (GTV), 14-31–14-32, 14-72Grove, Andy, 16-2GUTs (grand unified theories), 3-4

Hhalf-beam blocking, 13-2half-life, 3-14–3-17, 3-30t, 3-36, B-7thalf-value layer (HVL), 5-18–5-19, 5-27hand blocks, 13-3, 13-4f, 13-31HDR (high dose rate) brachytherapy, 3-13–3-14HDR (high dose rate) remote afterloader, 16-2,

16-37–16-40, 16-37f, 16-40fadvantages of, 16-40disadvantages of, 16-40

HDR (high dose rate) unitsdefined, 16-43safety precautions for, 17-26

HDR (remote afterloading units), 18-14–18-15HDR units accident, 18-22–18-23head holders, 14-68fhead scatter, 12-5–12-8, 13-27heavy charged particles

defined, 6-14interactions, 6-20–6-21

heel effect, 4-6, 4-7f, 4-16helical tomotherapy, 20-7, 20-8f, 20-65Hertz, Heinrich, 2-17Hi-Art® system, 20-7high dose rate (HDR) brachytherapy, 3-13–3-14high dose rate (HDR) remote afterloader, 16-2,

16-37–16-40, 16-37fhigh dose rate (HDR) units

defined, 16-43safety precautions for, 17-26

Hounsfield, G. N., 19-10Hounsfield units (HU), 19-21–19-23HVL (half-value layer), 5-18–5-19, 5-27HVL2 (second half-value layer), 5-27hydroxyl radical, 7-23hypotenuse, triangle, 1-11

IIBA isochronous cyclotron, 20-48fIC (internal conversion), 3-19–3-20, 3-25, 3-37ICRP (International Commission on Radiation

Protection), 17-1ICRU (International Commission on Radiation

Units and Measurements), 11-2, 14-31, 18-1image fusion, 19-32–19-33image-guided radiation therapy (IGRT),

19-42–19-46, 19-50imaging

See also CT (computed tomography)conventional simulators, 19-7–19-10digital images, 19-3–19-7functional/metabolic imaging, 19-36–19-39image fusion/registration, 19-32–19-33image-guided radiation therapy (IGRT),

19-42–19-46, 19-50magnetic resonance imaging (MRI),

19-27–19-31overview, 19-1–19-3portal, 19-39–19-42stereotactic radiosurgery (SRS), 20-37–20-38ultrasound imaging, 19-34–19-36

IMAT (intensity modulated arc therapy), 14-43,20-10, 20-65

immobilization devices, 14-67–14-71implant dosimetry systems

accumulated dose from implants, 16-20–16-21defined, 16-42linear array, 16-22–16-24planar and volume implants, 16-24–16-28, 16-29fpoint source, 16-21–16-22

implantable cardioverter-defibrillators, 18-21IMRT (intensity modulated radiation therapy),

20-1–20-27aperture-based optimization, 20-22delivery techniques, 20-6–20-11inverse planning issues, 20-18–20-21inverse treatment planning, 20-11–20-18physics plan validation, 20-22–20-25prostate cancer case study, 20-21whole-body dose and shielding, 20-25–20-27

in vivo dosimetry, 18-17–18-19indirect mechanism, 7-22–7-23indirectly ionizing, 6-1inelastic collision, 6-13infrared radiation, 2-18inherent filtration (self-filtration), 5-6, 5-9, 5-26inhomogeneities

electron beam dosimetry, 15-18–15-20photon beam dosimetry, 14-50–14-58, 14-73proton radiotherapy, 20-58–20-59

inscatter, electrons, 15-8fintensity maps, IMRT, 20-2f, 20-3f, 20-65intensity modulated arc therapy (IMAT), 14-43,

20-10, 20-65intensity, x-rays, 5-26

INDEX I-7

interface effects, 14-51interfractional uncertainty, 14-33interlocks, linear accelerators, 9-24–9-26internal (motorized) wedge, 14-20internal blocking, electron beam dosimetry,

15-14–15-16internal conversion (IC), 3-19–3-20, 3-25, 3-37internal margin, 14-33internal target volume (ITV), 14-33International Commission on Radiation

Protection (ICRP), 17-1International Commission on Radiation Units and

Measurements (ICRU), 11-2, 14-31, 18-1International System of Units (Système

International d’Unités; SI), 2-1interstitial brachytherapy, 16-2intracavitary applicators, 16-8intracavitary brachytherapy, 16-2intraleaf transmission, 13-10intraluminal brachytherapy, 16-2inverse square factor (ISF), 15-9, 15-12–15-14,

15-24Inverse Square Law, 5-13f, 5-15, 5-26inverse treatment planning, 20-11–20-18, 20-66inverse trig functions, 1-16iodine-125, 3-1, 16-5, 16-41iodine-131, 3-1ion chamber calibration, 11-5–11-7ion pair, mean energy to produce, 6-20ionization chambers, 8-5–8-16

cavity ionization chambers, 8-8–8-12free-air ionization chamber, 8-6–8-8plane-parallel ion chambers (flat cavity),

8-15–8-16thimble chambers, 8-12–8-15

iridium-192 (Ir-192), 3-1, 16-6, 16-41irrational numbers, 1-4irregular fields

approximate methods for estimatingequivalent square, 13-13–13-17

defined, 13-31dose rate calculations, 13-10

ISF (inverse square factor), 15-9, 15-12–15-14,15-24

isobars, 3-2isocenter, medical linear accelerator, 9-2, 9-3fisochronous cyclotron, 20-49isodose charts, 14-2–14-6, 14-71isodose curves

for 15 MV beam, 14-22ffor 6 MV beam, 14-22fadding for parallel-opposed fields, 14-18fdefined, 15-23electron beam dosimetry, 15-16–15-18

isodose distributions, 14-17–14-18isodose shift method, 14-8–14-11isomeric transition, 3-20electromagnetic decay, 3-37

isomers, 3-3isotones, 3-3isotopes

brachytherapy, 16-2defined, 3-2, 3-35radiation therapy, 3-30tregulated by NRC or agreement states, 17-2t

ITV (internal target volume), 14-33

JJoint Commission on Accreditation of Health

Care Organizations (JCAHO), 18-2Joule, James, 2-5joule unit, 2-5

KK shell

electrons, 2-25transition from M shell, 2-27f

K-capture, 3-23K-40 (potassium-40), 17-7Kamerlingh-Onnes, H., 2-11kerma, 7-6–7-7, 7-9, 7-14, 7-23f, 7-24, 16-18kilovoltage radiation therapy x-ray tube, 4-10fkilovolts-peak (kVp), 4-4, 4-15kinetic energy, 2-5Kjellberg, Ray, 20-42klystrons, 9-14, 9-15f, 9-41kV cone beam imaging, linac, 19-43fkVp (kilovolts-peak), 4-4, 4-15

LLarge Hadron Collider (LHC), 20-50lasers, 18-6latency, 17-9, 17-42lateral beam spreading, proton radiotherapy,

20-52–20-55, 20-70Lauterbur, Paul, 19-27Lawrence, Ernest, 20-41, 20-46Lawrence, J. H., 20-41LDR (low dose rate) brachytherapy, 3-13, 16-4,

16-29, 16-32, 16-41–16-44leaf sequencing algorithm, IMRT, 20-10,

20-65leakage radiation, 17-32, 17-37, 17-43, 20-26Leksell Gamma Knife®. See Gamma Knife®

Leksell, Lars, 20-34, 20-42LET (linear energy transfer), 6-26LHC (Large Hadron Collider), 20-50light charged particles, 6-14light field, 13-4flight localizing system, 9-19linac. See linear acceleratorslinac dose calculations, normalization

conditions, 12-5flinac-based radiosurgery, 20-30–20-34linac-based SRS methods, 20-67line focus principle, 4-5–4-6, 4-16

I-8 INDEX

linear accelerators, 9-2–9-32, 9-41, 9-45auxiliary subsystems, 9-22–9-24calibration, 11-1–11-15calibration error incident, 18-22conventional, 20-6–20-7, 20-19, 20-27,

20-34, 20-65, 20-67dosimetry check, 18-8–18-10, 18-12–18-13interlocks and safety systems, 9-24–9-26leakage radiation, 20-26mechanical checks, 18-4–18-8, 18-10–18-12microwave power, 9-12–9-16with MLC, 20-6, 20-7, 20-33patient support assembly, 9-26quality assurance, 18-2–18-5safety checks, 18-10, 18-13shielding design, 17-32–17-40See stereotactic radiosurgery (SRS)tertiary collimators, 20-30See tomotherapytreatment head, 9-16–9-22

linear array (of sources), 16-22–16-24linear attenuation coefficient, 5-17, 5-20linear energy transfer (LET), 6-26linear interpolation, 10-18–10-19Lipowitz metal, 13-3liquid detectors, 8-38liquid dosimeters, 8-2, 8-36–8-37liquid helium, 2-11liquid nitrogen, 2-12lithium, 3-6localization port film, 19-40localizing lasers, 18-4logarithms, 1-7–1-10Loma Linda accelerator, 20-49longitudinal sound waves, 19-35flow dose rate (LDR) brachytherapy, 3-13, 16-4,

16-29, 16-32, 16-41–16-44

MM shell

electrons, 2-25transition to K shell, 2-27f

mA (tube current), 5-7f, 5-25magnet yoke, isochronous cyclotron, 20-49magnetic resonance imaging (MRI), 2-15,

19-27–19-31, 19-48–19-49magnetism, 2-14–2-16magnetron, 9-12, 9-13f, 9-40–9-41malfunction 54, 18-23–18-24man made radiation, 17-5t, 17-7Manchester system (Paterson-Parker), 16-26t,

16-27t, 16-31criticisms, 16-34

Mansfield, Peter, 19-27manual brachytherapy procedures, 17-22–17-24manual densitometer, 8-31fMapCHECK™ device, 20-24fMarsden, Ernest, 2-23

mass attenuation coefficient, 5-20–5-21, 5-27mass collisional stopping power, 6-16, 6-17fmass defect, 3-5–3-6mass radiative stopping power, 6-16, 6-17fmass stopping power, 6-26matter, 6-1–6-30

interaction of charged particles, 6-11–6-21interaction with radiation, 6-24–6-26neutron interactions, 6-21–6-24photon interactions, 6-2–6-12

Maxwell, James Clerk, 2-16Maxwell’s equations, 2-16Mayneord correction, 10-8maze, treatment rooms, 17-39MCNP (Monte Carlo n particle), 7-21mean free path, 7-18mean-life, 3-18, 3-37, 16-3measurement, radiation

See also gas ionization detectors; solid-statedetectors

absorbed dose to air, 7-13–7-14charged particle equilibrium, 7-4dose, 7-14–7-17dose buildup and skin sparing, 7-9–7-13exposure, 7-2–7-4Monte Carlo calculations, 7-20–7-22overview, 7-1, 8-38–8-43phantoms, 8-3–8-5photon interactions example, 7-17–7-20radiation dosimetry quantities, 7-4–7-9

mechanical checks, linear accelerators,18-4–18-8, 18-10–18-12

mechanical tolerances, linear accelerators,18-4, 18-5t

mechanics, 2-2–2-6Newton’s second law, 2-4–2-5power, 2-6work, 2-5work energy theorem, 2-5–2-6

medical electron linear accelerators. See linearaccelerators

medical events, 17-19medical radiation exposure, 17-7megaelectron volts (MeV), 3-5megavoltage photon beams

beam calibration, 11-4, 11-13beam quality, 11-8–11-9calibration conditions, 11-10–11-11constancy checks of beam calibration,

11-12–11-13ion chamber calibration, 11-5–11-7normalization conditions, 11-2–11-4overview, 11-14–11-15task group 51 dose equation, 11-9–11-10TG-51 calculation example, 11-11–11-12

metabolic imaging, 19-36–19-39metal oxide semiconductor-field effect transistors

(MOSFETs), 8-2, 8-34–8-36, 8-43

INDEX I-9

metastable nucleus, 3-20MeV (megaelectron volts), 3-5Mevalac, 12-6t, 12-11, 13-28, 14-66, 15-9

data tables, C-1–C-16definition, 12-5, 15-2, 15-5, 15-23depth of maximum buildup, 15-4, C-16dm values, 15-5t, 15-23t, C-16electron applicator factors, 15-9t, C-16normalization, 13-25OAR values, 13-24, 13-25t, C-12percent depth dose curves, 15-2fpercent depth dose values, 12-9, 15-2, 15-4,

C-2–C-5, C-15scatter correction factors, 12-6tSMR values, 13-18, 13-19, C-10–C-11TMR values, C-6–C-9tray factors, 13-5used in Examples, 6 MV beam, 12-12, 13-13,

13-16, 13-26, 13-27, 14-27, 14-65;18 MV beam, 12-10, 12-17

used in Problems, 12-19, 12-20, 13-33, 13-35,14-75–14-77, 15-25

value of µ, 13-19wedge factors, 14-24, C-13–C-14

microscopic biological damage, 7-22–7-23microscopic physics

bremsstrahlung emission, 5-4–5-5characteristic x-rays, 5-2–5-4

microtrons, 3-34microwave power, 9-12–9-16microwave wavelengths, 2-18microwaves, 2-18, 9-2, 9-7–9-15, 9-23, 9-40,

9-41, 20-32, 20-34, 20-68MIMiC system, 20-6, 20-7fmissing tissue compensator, 14-48, 14-50fwith MLC (multileaf collimator), 13-6–13-10,

13-31Mo-99, 3-29modalities, treatment. See IMRT (intensity

modulation in radiation therapy); protonradiotherapy; stereotactic radiosurgery (SRS)

modified Batho method, 14-55modulation wheel, 20-51fmodulator, 9-42mold room, 13-5, 18-20–18-21monitor unit (MU)

beam calibration, 11-1defined, 9-18dose rate calculations, 12-8–12-17,

13-10–13-31, 14-27, 15-9head scatter, 12-5–12-8normalization conditions, 11-2, 12-3–12-5overview, 12-1–12-3phantom scatter, 12-5–12-8

monoenergetic x-rays, 5-16–5-18Monte Carlo calculations, 7-20–7-22

using Peregrine software, 7-21fMonte Carlo n particle (MCNP), 7-21

Monte Carlo treatment planning, 7-20–7-22,20-60–20-61

MOSFETs (metal oxide semiconductor-fieldeffect transistors), 8-2, 8-34–8-36, 8-43

motorized wedge, 14-20MRI (magnetic resonance imaging), 2-15,

19-27–19-31, 19-48–19-49MU (monitor unit)

beam calibration, 11-1defined, 9-18dose rate calculations, 12-8–12-17,

13-10–13-31, 14-27, 15-9head scatter, 12-5–12-8normalization conditions, 11-2, 12-3–12-5overview, 12-1–12-3phantom scatter, 12-5–12-8

multileaf collimator (MLC), 13-6–13-10, 13-31multiple beam, dose distributions, 14-28–14-31multiplication, 1-3multi-slice CT scanner, 19-16fMUPIT perineal interstitial template, 16-9fMV (megavoltage) x-ray beams, 7-10, 9-6, 9-41,

11-5, 11-8mycosis fungoides, 15-1

Nnarrow beam attenuation, 5-17f

defined, 5-27of monoenergetic x-rays, 5-16–5-18

National Council on Radiation Protection(NCRP), 17-1

National Institute for Standards and Technology(NIST), 8-6, 11-5

natural log, 1-8natural radiation, 17-5tNCRP (National Council on Radiation

Protection), 17-1negligible individual risk level (NIRL), 17-16net optical density, 8-30neutrino, 3-10t, 3-22neutrons

activation, 3-32–3-34defined, 17-44interactions with matter, 6-21–6-24properties of, 3-10tshielding design for linear accelerators, 17-39

newton, 2-1Newton’s second law, 2-4–2-5nickel-titanium “superelastic” alloy, 16-38NIRL (negligible individual risk level), 17-16NIST (National Institute for Standards and

Technology), 8-6, 11-5nominal accelerating potential, 11-8nonconducting window, linear accelerators, 9-24non-coplanar beams, 14-28, 14-30non–tissue-equivalent build-up material, 18-17normal tissue complication probability

(NTCP), 14-40

I-10 INDEX

normalization conditions, 11-2for Co-60, 11-3defined, 11-14for linear accelerators, 11-3–11-4monitor unit (MU), 12-3–12-5

NRC. See Nuclear Regulatory CommissionNTCP (normal tissue complication

probability), 14-40nuclear binding energy, 3-5–3-6, 3-35nuclear de-excitation, 3-19, 3-37nuclear fission, 3-7, 3-30nuclear fusion, 3-7Nuclear Regulatory Commission. See NRC

(Nuclear Regulatory Commission)Nuclear Regulatory Commission (NRC), 3-32,

11-2, 17-15–17-27annual dose limits, 17-15–17-16events reported, 17-20–17-22ion chamber calibration, 8-13medical license and general requirements,

17-17–17-18quality assurance, 18-2, 18-13–18-15radiation protection, 17-1, 17-22–17-24safety precautions for Co-60 units,

17-26–17-27safety precautions for HDR units, 17-26timer error, 9-30written directives and medical events,

17-18–17-20nuclear stability, 3-6–3-8, 3-35nuclei properties, 3-2–3-3, 3-9–3-10nucleons, 3-2nucleus, 2-23

OOAR (off-axis ratio), 13-23–13-25ODI (optical distance indicator), 9-20f, 18-8“off cord” irradiation field, 13-16foff-axis ratio (OAR), 13-23–13-25one-dimensional dose correction methods, 14-52open fields, dose rate calculations, 13-10optical density, 8-29–8-30, 8-42optical distance indicator (ODI), 9-20f, 18-8optimization, inverse treatment planning, 20-12oral stents, 15-14organs at risk, 14-32orthogonal fields, 14-74orthogonal films, 16-31, 16-36forthovoltage x-ray beams, 4-4outscatter, electrons, 15-8fovertravel, 13-10ovoids, Fletcher-Suit applicator, 16-29–16-30,

16-30f

Ppacemakers, 18-21PACS (picture archiving and communication

system), 19-7

pair production, 6-2, 6-3f, 6-9–6-10, 6-25palladium-103 (Pd-103), 3-1, 16-7, 16-41parallel-opposed fields, 14-14–14-20

adding isodose distributions, 14-17–14-18beam weighting, 14-18–14-20

parent nucleus, 3-10particle accelerators, 3-11, 3-30, 3-34,

3-39, 9-41particles

heavy charged, 6-20–6-21properties, 3-9–3-10

passive scattering, 20-52–20-54, 20-70past pointing, 14-41patch field, 20-61fPaterson-Parker system, 16-25–16-26,

16-29f, 16-30patient positioning, 14-67–14-71patient safety

implantable cardioverter-defibrillators, 18-21pacemakers, 18-21quality assurance (QA), 18-15–18-19radiation therapy accidents, 18-22–18-24starting new treatment programs, 18-20

patient support assembly, linear accelerator, 9-26Pauli, Wolfgang, 3-21Pd-103 (palladium-103), 3-1, 16-7, 16-41PDD. See percent depth dosePDR (pulsed dose rate) remote afterloaders, 16-2peak scatter factor (PSF), 10-13–10-14pendant, medical linear accelerator, 9-3fpenumbra, 9-35–9-36, 9-38–9-39, 9-42percent depth dose (PDD), 10-4–10-10, 10-20,

11-8, 12-3, 15-2permanent implants

accumulated dose from, 16-20–16-21mean-life, 3-18

permanent magnets, 2-14–3-15personnel monitoring, 17-27–17-30PET (positron emission tomography), 3-23

defined, 19-49glucose metabolism rates and, 19-36

PET/CT unit, 19-38fphantom scatter, 12-5–12-8, 13-26–13-27phantoms, 8-3–8-5, 8-38photoelectric effect, 6-4–6-5, 6-24photomultiplier tube (PMT), 8-42photon beams, megavoltage

beam calibration, 11-4, 11-13beam quality, 11-8–11-9calibration conditions, 11-10–11-11characteristics, 9-31–9-40constancy checks of beam calibration,

11-12–11-13ion chamber calibration, 11-5–11-7normalization conditions, 11-2–11-4overview, 11-14–11-15Task Group 51 dose equation, 11-9–11-10TG-51 calculation example, 11-11–11-12

INDEX I-11

photon interactionsexample, 7-17–7-20matter, 6-2–6-12

photonsdefined, 2-19emission, 2-26penetration range, 15-2

photonuclear reactions, 6-11, 6-25physical penumbra, 9-36, 9-39physical quality assurance

dosimetry instrumentation, 18-15linear accelerators, 18-4–18-13NRC regulations pertaining to, 18-13–18-15

physics chart checks, 18-15–18-17physics plan validation, IMRT, 20-22–20-25picture archiving and communication system

(PACS), 19-7picture elements (pixels), 19-4Pi-mesons, 3-10tpions, 3-10tPITV (prescription isodose to target

volume), 20-39pixels (picture elements), 19-4plan validation, IMRT, 20-66planar implants, 16-24–16-28, 16-29fplanchet, TLD reader, 8-28Planck’s constant, 2-20plane-parallel ion chambers (flat cavity),

8-15–8-16, 11-13planning organ at risk volume (PRV), 14-32planning target volume (PTV), 14-31–14-32, 14-72“plum pudding” model, 2-22PMT (photomultiplier tube), 8-42point source, 5-14, 16-21–16-22point-to-point matching, image registration, 19-32polyenergetic x-rays, 5-17polymer gels, 8-2, 8-43portal imaging, 18-17

defined, 19-49electronic portal imaging devices (EPIDs),

19-40–19-42port films, 19-40

position aids, 14-67–14-68positional uncertainty, 14-33positive integer, defined, 1-2positron decay (β+ decay), 3-23, 3-25fpositron emission tomography (PET), 3-23,

19-36–19-37defined, 19-49glucose metabolism rates and, 19-36

positrons, 3-9–3-10tpotassium-40 (K-40), 17-7potential difference, electricity, 2-10–2-12pound unit, 2-4power, 2-6, 9-12–9-14, 9-40, 9-41, 18-6, 18-14power (exponent), 1-2, 2-6power law method (modified Batho method), 14-55prescription dose, 14-38, 15-23

prescription isodose to target volume (PITV), 20-39prescription point, 12-2, 15-4primary barriers, 17-33–17-36, 17-44primary radiation, 4-11, 17-32, 17-43primary radiation contribution, 10-2–10-3product raised to a power, 1-4propeller (modulation wheel, ridge filter), 20-51fproportional counters, 8-2, 8-21–8-22, 8-40proportionality constant λ, 3-12prospective gated imaging, 4D CT, 19-25, 19-26fprostate cancer, 16-2proton laser accelerators, 20-64proton radiotherapy, 20-41–20-65

accelerators, 20-44–20-51beam delivery/transport, 20-55–20-56calibration of proton beams and quality

assurance, 20-63dielectric wall accelerators, 20-64–20-65dose calculations and treatment planning,

20-56–20-61dose distributions, 20-61–20-62lateral beam spreading and field shaping,

20-52–20-55overview, 20-41–20-42potential advantages, 20-42–20-44production and selection of different energy

beams, 20-51–20-52proton laser accelerators, 20-64superconducting cyclotrons, 20-64

proton synchrotron, 20-50fPRV (planning organ at risk volume), 14-32PSF (peak scatter factor), 10-13–10-14PTV (planning target volume), 14-31–14-32, 14-72pulsed dose rate (PDR) remote afterloaders, 16-2Pythagorean theorem, 1-11

QQA (quality assurance)

patient safety, 18-15–18-20stereotactic radiosurgery (SRS), 20-40–20-41

quantum chromodynamics, 3-4quantum mechanics, 2-24, 3-11quarks, 2-7quenching, 8-24Quimby, Edith, 16-25Quimby system, 16-25

RR&V (record and verify) software, 18-16Ra-226 (radium), 16-3, 16-41radians, 1-15radiation dosimetry quantities, 7-4–7-9radiation exposure report, 17-4, 17-30tradiation monitor, 17-25fradiation protection

annual dose limits, 17-15–17-16biological effects of radiation, 17-8–17-14brachytherapy procedures, 17-22–17-24

I-12 INDEX

dosimetric quantities used for, 17-3–17-5events reported, 17-20–17-22exposure of individuals to radiation,

17-5–17-8medical events, 17-19–17-20medical license and general requirements,

17-17–17-18personnel monitoring, 17-27–17-30principles, 17-14–17-15, 17-41shielding design for linear accelerators,

17-32–17-40shipment and receipt of radioactive packages,

17-31–17-32for therapy units, 17-24–17-27written directives, 17-18–17-19

Radiation Safety Officer (RSO), 17-17radiation therapy accidents, 18-22–18-24

Co-60 overdose, 18-24HDR accident, 18-22–18-23linear accelerator calibration error, 18-22Malfunction 54, 18-23–18-24

Radiation Therapy Oncology Group (RTOG),11-13, 20-39

radiative loss, 6-15radio waves, 2-17radioactive decay, 3-7, 3-11–3-13, 3-19, 3-37radioactive equilibrium, 3-26–3-30Radioactive White I label, 17-31Radioactive Yellow II label, 17-31Radioactive Yellow III label, 17-31radioactivity

See also atomic nucleioverview, 3-10–3-39, 16-2–16-3sources of, 16-3–16-7

radiochromic film, 8-33See also GAFChromic film

radiographic medical exams (effective dose), 17-8tradioisotopes, 3-11, 3-30, 3-35, 16-3, 17-2

See also radionuclidesRadiological Physics Center (RPC), 11-13, 20-40

mailed dosimetry program, 11-13radionuclides

See also radioisotopesdefined, 3-35fission byproducts, 3-30–3-32neutron activation, 3-32–3-34particle accelerators, 3-34sources of, 3-39

radium (Ra-226), 16-3, 16-41decay, 3-28ratio of activity of radon to, 3-28f

radon, 3-27, 3-28f, 17-7RANDO® phantom, 8-4–8-5range, 6-18–6-20, 6-26range finder, 18-8ratio of TAR (rTAR) method

dose corrections, 14-52, 14-54skin contour, 14-12–14-13

ready pack film, 18-11receipt, radioactive packages, 17-32recoil protons, 6-23recombination, 8-19, 8-20f, 8-40record and verify (R&V) software, 18-16rectifier, 4-4registration, image, 19-32–19-33relative dose distribution, 10-3, 16-5, 16-15, 19-19relaxation, MR imaging, 19-30remote afterloading units (HDR), 18-14–18-15resistor, 2-9rest mass, 2-21–2-22restricted stopping power, 6-26retrospective correlation, 4D CT, 19-25, 19-27fridge filter, 20-51fright triangle, 1-11fright-hand rule, 2-16ring and tandem applicator, 16-9fring badge, radiation, 17-28f, 17-29“roentgens to rads” conversion ratio, 7-16Röntgen, Wilhelm Conrad, 4-1, 5-22–5-24rotating anode, 4-7f, 4-16rotating anode x-ray tube, 4-8frotation therapy, 14-41–4-43rotor, x-ray machine, 4-6RPC (Radiological Physics Center), 11-13, 20-40

mailed program, dosimetry, 11-13RSO (Radiation Safety Officer), 17-17rTAR (ratio of TAR) method. See ratio of TAR

(rTAR) methodRTOG (Radiation Therapy Oncology Group),

11-13, 20-39Rutherford, Ernest, 2-23

SSAD (source-to-axis distance), 9-2, 9-5f, 9-41,

10-3, 10-12safety

See also radiation protectionimplantable cardioverter-defibrillators,

18-21linear accelerators, 9-24–9-26, 18-4–18-5t,

18-10, 18-13mold room, 18-20–18-21pacemakers, 18-21quality assurance (QA), 18-15–18-19radiation therapy accidents, 18-22–18-24

sagittal lasers, 18-5sample volume, 8-7scanner, single-slice, 19-13scanning water phantom, 10-7scatter component, whole-body dose, 20-26scatter correction factors, 12-6t, 12-11

collimator, 12-7phantom, 12-7, 12-13

scatter radiation, 4-12f, 10-2–10-3, 13-11–13-12,17-37–17-39, 17-43

scattering, photons, 5-13, 5-16, 5-26

INDEX I-13

scientific calculator, 1-1scintillation, 8-2screens, x-ray, 4-10–4-13, 4-17sealed sources, 16-3

defined, 16-41medical event for, 17-19

second half-value layer (HVL2), 5-27secondary barriers, 17-33, 17-34f, 17-37–17-39,

17-44secondary electrons, 4-9secular equilibrium, 3-27–3-28, 3-39seed applicators, 16-8segmental MLC (SMLC), 20-65segmental multileaf IMRT (SMLC), 20-10self-filtration (inherent filtration), 5-6, 5-9, 5-26serial organ, 14-32–14-33serial tomotherapy, 20-6–20-7, 20-65setup margin, 14-33shaped fields. See also field shaping

asymmetric jaws, 13-2–13-3cast blocks, 13-3–13-6dose rate calculations, 13-10–13-31hand blocks, 13-3multileaf collimators, 13-6–13-10overview, 13-1–13-2

shell structure, carbon atom, 2-25fshielding barriers, 17-33shielding design for linear accelerators, 17-32–17-40

entryway, 17-39–17-40neutrons, 17-39primary barriers, 17-35–17-36secondary barriers, 17-37–17-39

shielding factor, radiation exposure, 17-14shipping radioactive packages, 17-31–17-32

NRC regulations for receiving, 17-32package labels, 17-31

SI (Système International d’Unités; InternationalSystem of Units), 2-1

prefixes, 2-2tunits, 2-2t, 3-36

side cavity coupling, 9-10side lasers, 18-5–18-7sievert integral, 16-17similar triangles, 1-11, 1-12fsimple immobilization devices, 14-68simulated annealing, 20-16simulators, conventional, 19-7–19-10sine function, 1-14single beams, 14-14single linear array of sources, 16-22single-slice scanner, 19-13skin contour, 14-6–14-13

defined, 14-71effective SSD method, 14-11–14-12isodose shift method, 14-8–14-11ratio of TAR (rTAR) method, 14-12–14-13

skin dose, 14-43–14-46, 14-48, 14-68, 14-72,18-17–18-18

slice, image, 19-6SMLC (segmental MLC), 20-65SMLC (segmental multileaf IMRT), 20-10SOBP (spread-out Bragg peak), 20-43soft collisions, 6-14solid air shell, 8-10fsolid phantom, 11-13solid-state detectors, 8-2, 8-25–8-36, 8-38

diodes, 8-33–8-34film, 8-29–8-33MOSFETs, 8-34–8-36thermoluminescent dosimeters (TLDs),

8-25–8-29source accounting, 17-24source strength, brachytherapy, 16-10–16-13, 17–18source-to-axis distance (SAD), 9-2, 9-5f,

9-41, 10-3, 10-12source-to-surface distance (SSD), 9-3, 9-5, 9-20,

9-33, 9-36–9-38, 9-41–9-43, 10-3special theory of relativity, 2-20–2-22specific activity, 3-14, 16-3–16-4, 16-6, 16-38,

16-41spreading of the beam, 5-13, 5-26spread-out Bragg peak (SOBP), 20-43Sr-90 (strontium-90), 3-1, 16-6, 16-42SRS (stereotactic radiosurgery). See stereotactic

radiosurgery (SRS)SRS head frame, 20-30SSD (source-to-surface distance), 9-3, 9-5, 9-20,

9-33, 9-36–9-38, 9-41–9-43, 10-3stable nuclei, 3-8f, 3-8t, 3-35standing wave linac, 9-9stated beam energy (nominal accelerating

potential), 11-8stationary anode, 4-7fstepped leaves, MLC, 13-11fstereo shift method, 16-36, 16-37fstereotactic radiosurgery (SRS), 20-27–20-41

CyberKnife®, 20-39, 20-34, 20-68dosimetry, 20-40Gamma Knife®, 20-34–20-37, 20-67imaging, 20-37–20-38linac-based radiosurgery, 20-30–20-34overview, 20-27–20-30quality assurance (QA), 20-40–20-41treatment planning, 20-38–20-40

stochastic effects, 17-9, 20-15stopping power, 6-15–6-18, 6-25–6-26,

20-59–20-60string theory, 3-5strong nuclear force, 3-3, 3-35strontium-90 (Sr-90), 3-1, 16-6, 16-42Styrofoam block, 13-6fsuperconducting cyclotrons, 20-64superconductors, 2-11superficial beams, 4-4, 5-27Superflab, 14-47surface dose, 14-44–14-46

I-14 INDEX

Surface matching, image registration, 19-32survey meter ion chambers, 8-16–8-17, 8-17fsurvey meters, 8-38symmetric jaws, central axis, 13-10–13-22symmetry, beam, 18-13synchrotrons, 3-34, 20-49–20-51, 20-70

Ttandem, Fletcher-Suit applicator, 16-28,

16-30f, 16-30ftandem and ovoid, 16-29–16-34, 16-33ftangent function, 1-14TAR (tissue-air ratio), 10-4, 10-11–10-12, 10-13,

10-15, 10-16, 10-18, 10-20–10-21, 12-3,14-12, 14-52–14-53, 14-73

target compositiondefined, 4-3effect on x-ray spectrum, 5-8f, 5-26

target, defined, 4-16Tc-99m (technetium-99m), 3-29TCP (tumor control probability), 14-40teletherapy, 3-1, 9-1temporary implants, 16-20–16-21, 17-23temporary interstitial implants, 16-6tenth-value layers (TVLs), 17-35tertiary field-shaping device, 13-9TF (tray factor), 13-5TG-21 (Task Group 21), 11-2, 11-6TG-43 (Task Group 43), 16-18–16-20TG-51 (Task Group 51), 11-6, 11-9–11-10,

14–15, 18-22protocol, calibrating 10 MV beams, 11-11

theory of everything, 3-4therapy x-ray tubes

defined, 4-15versus diagnostic tubes, 4-17overview, 4-9–4-10

thermal neutrons, 3-33thermionic emission, 4-3thermoluminescent dosimeters (TLDs), 8-2,

8-25–8-29, 8-41thermoplastic mask, 14-71fthermoplastic materials, 14-69thimble chambers, 8-12–8-15, 8-39Thompson, J. J., 2-22, 5-22Thorium decay series, 3-11three-beam arrangement, 14-30, 14-31fthree-dimensional dose correction method, 14-52thyratron, 9-15TI (transport index), 17-31time dilation, 2-20time factor, radiation exposure, 17-14timer error, Co-60 units, 9-29–9-30, 9-42timer setting, open fields, 12-1–12-20

dose rate calculations, 12-8–12-17head scatter and phantom scatter, 12-5–12-8normalization conditions, 12-3–12-5overview, 12-1–12-3

tissue compensators, 14-48–14-50tissue inhomogeneities, 14-50–14-58, 14-73tissue/lead interface, 15-15ttissue-maximum ratio (TMR), 10-11, 14–16, 12-3tissue-phantom ratio (TPR), 10-14–10-16tissue-to-air ratio (TAR), 10-11–10-12, 12-3TLD reader, 8-28fTLDs (thermoluminescent dosimeters), 8-2,

8-25–8-29, 8-41TMR (tissue-maximum ratio), 10-11,

10-14–10-16, 12-3Tobias, C. A., 20-41tomotherapy, 14-43, 20-6–20-7, 20-8f, 20-65tongue and groove leaves, MLC, 13-11ftotal mass absorption coefficient, 6-11TPR (tissue-phantom ratio), 10-14–10-16transducer, ultrasound, 19-36transient effects (pacemakers), 18-21transient equilibrium, 3-28–3-30, 3-39transmission factor, wedges, 14-24–14-27transmission penumbra, 9-38transmission waveguides, 9-24transport index (TI), 17-31traveling wave linac, 9-7tray factor (TF), 13-5treatment head, dual photon energy linear

accelerator, 9-4ftreatment head, linear accelerators, 9-16–9-22

bending magnets, 9-22electron therapy mode, 9-21–9-22x-ray mode, 9-17–9-21

treatment plan, 12-2treatment planning, 7-21

HDR system workstation, 16-38NRC regulations, 18-15proton radiotherapy, 20-56–20-61stereotactic radiosurgery (SRS), 20-38–20-40

treatment rooms, 17-39triangles, similar, 1-11, 1-12ftriaxial cable, 8-17trigonometry, 1-14–1-16tritium, 3-2tube current (mA), 5-7f, 5-25tube voltage, 4-3, 5-8f, 5-25tubes, x-ray, 4-2–4-10, 4-15, 4-17tumor control probability (TCP), 14-40tungsten atom, 2-26ftungsten eye shields, 15-16fTVLs (tenth-value layers), 17-35

Uultrasound imaging, 19-34–19-36, 19-49ultraviolet (UV) radiation, 2-19

UVA band, ultraviolet spectrum, 2-19UVB band, ultraviolet spectrum, 2-19UVC band, ultraviolet spectrum, 2-19

uncertainties, positional, 14-33uncontrolled area, 17-43

INDEX I-15

unfiltered bremsstrahlung, 5-6funiform-density tissue, 14-50universal speed limit, 2-20–2-21unknowns, TLD, 8-26uranium decay series, 3-11

Vvaginal cylinder, 16-8fvector, defined, 2-2velocity, defined, 2-3verification port film, 19-40virtual simulation, CT, 19-24virtual source distance (VSD), 15-11–15-12,

15-24voltage waveforms, 5-9fvoltmeter, 2-11volume implants, 16-24–16-28voxels (volume elements), 14-36voxel-to-voxel matching, image

registration, 19-32VSD (virtual source distance), 15-11–15-12,

15-24

Wwall-mounted radiation monitor, 17-25fwater phantom beam scanner, 9-32fwater phantoms, 8-4, 11-13water-cooling system, linear accelerators, 9-24waveguide

accelerating, 9-2, 9-4f, 9-7–9-12, 9-14, 9-16,9-22–9-24, 9-41

transmission, 9-15, 9-24wavelength, light, 2-17weak nuclear force, 3-4wedged pair, 14-25fwedges, 14-20–14-28

defined, 14-71dose rate calculations with, 14-27–14-28intensity modulation, 20-6transmission factor, 14-24–14-27wedged fields, 14-24

weight of object, 2-4weight, sources, 16-24fweighting factor

radiation, 17-4ttissue, 17-5t

well chambers, 8-40well-ionization chambers, 8-12whole brain irradiation field, 13-16fwhole-body dose, IMRT, 20-25–20-27Wilson, Robert, 20-41, 20-42fwork, 2-5work-energy theorem, 2-5–2-6, 4-3

Xxenon-124 (Xe-124), 16-5x-ray attenuation, 5-12–5-18

attenuation by matter, 5-16–5-18beam divergence, 5-14–5-16Inverse Square Law, 5-14–5-16

x-ray–based frameless imaging systems, 20-30x-ray fluorescence, 5-3x-ray generator, defined, 4-17x-ray mode, linear accelerators, 9-17–9-21, 15-11x-ray production

attenuation, 5-12–5-18directional dependence of bremsstrahlung

emission, 5-12efficiency of, 5-10–5-12film and screens, 4-10–4-13generator, 4-13–4-15half-value layer (HVL), 5-18–5-19mass attenuation coefficient, 5-20–5-21microscopic physics, 5-1–5-5overview, 4-1–4-2Röntgen, Wilhelm Conrad, 5-22–5-24spectrum, 5-5–5-10superficial therapy x-ray machine, 4-4f

x-ray spectrum, 5-5–5-10x-ray tube. See therapy x-ray tubesXVI (x-ray volume imaging) system, 19-45f

I-16 INDEX

Documents

10.250 in 1.690 in theRapy - Medical Physics on Field Size and SSD . . . . . . . . . . . . . . . . . . . . . . 10-10 ... (SSD = SAD) ... 12.4.4 The Equivalence of PDD and TMR Calculations